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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 17 Perimeter and Areas of Plane Figures

Chapter 17 – Perimeter and Areas of Plane Figures Exercise Ex. 17A

Question 1

Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14. 5 cm.

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 2

Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Hence, find the height corresponding to the longest side.

Solution 2

Let a = 42 cm, b = 34 cm and c = 20 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

(i)Area of triangle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

(ii)Let base = 42 cm and corresponding height = h cm

          Then area of triangle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

          Hence, the height corresponding to the longest side = 16 cm

Question 3

Calculate the area of the triangle whose sides are 18 cm, 24 cm and 30 cm in length. Also, find the length of the altitude corresponding to the smallest side of the triangle.

Solution 3

Let a = 18 cm, b = 24 cm, c = 30 cm

Then,2s = (18 + 24 + 30) cm = 72 cm

           s = 36 cm

(s a) = 18cm, (s b) = 12 cm and (s c) = 6 cm

(i)Area of triangle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

(ii)Let base = 18 cm and altitude = x cm

          Then, area of triangle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

           Hence, altitude corresponding to the smallest side = 24 cm

Question 4

The sides of a triangle are in the ratio 5 : 12 : 13, and it perimeter is 150 m. find the area of the triangle.

Solution 4

On dividing 150 m in the ratio 5 : 12 : 13, we get

Length of one side = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of the second side = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of third side = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Let a = 25 m, b = 60 m, c = 65 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

(s a) = 50 cm, (s b) = 15 cm, and (s c) = 10 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, area of the triangle = 750 m2

Question 5

The perimeter of a triangular field is 540 m, and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. Also, find the cost of ploughing the field at Rs. 18. 80 per R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 5

On dividing 540 m in ratio 25 : 17 : 12, we get

Length of one side = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of second side = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of third side = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures=120 m

Let a = 250m, b = 170 m and c = 120 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Then, (s a) = 29 m, (s b) = 100 m, and (s c) = 150m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

The cost of ploughing 100 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresarea is = Rs. 18. 80

The cost of ploughing 1 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresis = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

The cost of ploughing 9000 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresarea = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                                                      = Rs. 1692

Hence, cost of ploughing = Rs 1692.

Question 6

The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.

Solution 6

Let the length of one side be x cm

Then the length of other side = {40 (17 + x)} cm = (23 – x) cm

Hypotenuse = 17 cm

Applying Pythagoras theorem, we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, area of the triangle = 60 cm2

Question 7

The difference between the sides at right angles in a right – angled triangle is 7 cm. The area of the triangle isR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures. Find its perimeter.

Solution 7

Let the sides containing the right – angle be x cm and (x – 7) cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

One side = 15 cm and other = (15 – 7) cm = 8 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresperimeter of triangle (15 + 8 + 17) cm = 40 cm

Question 8

The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures, find the perimeter of the triangle.

Solution 8

Let the sides containing the right angle be x and (x 2) cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

One side = 8 cm, and other (8 2) cm = 6 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                      = 10 cm

Therefore, perimeter of the triangle = 8 + 6 + 10 = 24 cm

Question 9

Each side of an equilateral triangle is
10 cm. Find

(i) the area of a triangle and (ii) the height of the
triangle.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 10

The height of an equilateral triangle measures 9 cm. Find its area, correct to 2 places of decimal. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 10

Let each side of the equilateral triangle be a cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 11

If the area of an equilateral triangle is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresfind its perimeter.

Solution 11

Let each side of the equilateral triangle be a cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Perimeter of equilateral triangle = 3a = (3 12) cm = 36 cm

Question 12

If the area of an equilateral triangle is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresfind its height.

Solution 12

Let each side of the equilateral triangle be a cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresarea of equilateral triangle =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Height of equilateral triangle

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 13

The base of a right – angled triangle measures 48 cm and its hypotenuse measures 50 cm. Find the area of the triangle.

Solution 13

Base of right angled triangle = 48 cm

Height of the right angled triangle =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 14

The hypotenuse of a right – angled triangle measure 6.5 m and its base measures 6 m. Find the length of perpendicular, and hence calculate the area of the triangle.

Solution 14

Let the hypotenuse of right – angle triangle = 6.5 m

Base = 6 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, perpendicular = 2.5 cm and area of the triangle =7.5 cm2

Question 15

Find the area of a right – angled triangle, the radius of whose circumcircle measure 8 cm and the altitude drawn to the hypotenuse measure 6 cm.

Solution 15

The circumcentre of a right – triangle is the midpoint of the hypotenuse

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hypotenuse = 2 × (radius of circumcircle)

= (2 × 8) cm = 16 cm

Base = 16 cm, height = 6 cm

Area of right angled triangle

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, area of the triangle= 48 cm2

Question 16

Find the length of the hypotenuse of an isosceles right × angled triangle whose area is 200 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures. Also, find the perimeter. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures.

Solution 16

Let each equal side be a cm in length.

Then,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, hypotenuse = 28.28 cm and perimeter = 68.28 cm

Question 17

The base of an isosceles triangle measure 80 cm and its area is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures. Find the perimeter of the triangle.

Solution 17

Let each equal side be a cm and base = 80 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresperimeter of triangle = (2a + b) cm

= (2 41 + 80) cm

= (82 + 80) cm = 162 cm

Hence, perimeter of the triangle = 162 cm

Question 18

Each of the equal sides of an isosceles triangle measures 2 cm more than its height, and the base of the triangle measure 12 cm. Find the area of the triangle.

Solution 18

Let the height be h cm, then a= (h + 2) cm and b = 12 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Squaring both sides,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Therefore, a = h + 2 = (8 + 2)cm = 10 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, area of the triangle = 48 cm2.

Question 19

In the given figure, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC is an equilateral triangle the length of whose side is equal to 10 cm, and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC is right angled triangle at D and BD = 8 cm. Find the area of the shaded region. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of shaded region = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC – Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC

First we find area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Second we find area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC which is right angled

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of shaded region = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC – Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC

= (43.30 – 24) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 19. 30 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of shaded region = 19.3 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 20

Find the area and perimeter of an isosceles right – angled triangle, each of whose equal sides measures 10 cm. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 20

Let R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC is a isosceles triangle. Let AC, BC be the equal sides

Then AC = BC = 10cm. Let AB be the base of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC right angle at C.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of right isosceles triangle ABC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, area = 50 cm2 and perimeter = 34.14 cm

Chapter – Exercise

Solution 1
Solution 2
Solution 3

Chapter 17 – Perimeter and Areas of Plane Figures Exercise FA

Question 1

In the given figure ABCD is a quadrilateral in which ABC = 90, BDC = 90, AC = 17 cm, BC= 15 cm, BD = 12 cm and CD = 9cm. The area of quad. ABCD is

  1. 102 cm2
  2. 114 cm2
  3. 95 cm2
  4. 57 cm2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 2

In the given figure ABCD is a trapezium in which AB = 40 m, BC = 15 m, CD = 28 m, AD = 9 m and CE ^ AB. Area of trap. ABCD is

  1. 306 m2
  2. 316 m2
  3. 296 m2
  4. 284 m2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 3

The sides of a triangle are in the ratio 12:14:25 and it perimeter is 25.5 cm. The largest side of the triangle is

  1. 7 cm
  2. 14 cm
  3. 12.5 cm
  4. 18 cm
Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 4

The parallel sides of trapezium are 9.7 cm and 6.3 cm, and the distance between them is 6.5 cm. The area of the trapezium is

  1. 104 cm2
  2. 78 cm2
  3. 52 cm2
  4. 65 cm2
Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 6

Find the area of an isosceles triangle each of whose equal sides is 13 cm and whose base is 24 cm.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 7

The longer side of a rectangular hall is 24 m and the length of its diagonal is 26 m. Find the area of the hall.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

Question 8

The length of the diagonal of a square is 24 cm. Find its area.

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 9

Find the area of a rhombus whose diagonals are 48 cm and 20 cm long.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 10

Find the area of a triangle whose sides are 42 cm, 34 cm and 20 cm.

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 11

A lawn is in the form of a rectangle whose sides are in the ratio 5:3 and its area is 3375 m2. Find the cost of fencing the lawn at Rs.20 per metre.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 12

Find the area of a rhombus each side of which measures 20 cm and one of whose diagonals is 24 cm.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 13

Find the area of a trapezium whose parallel sides are 11 cm and 25 cm long and non-parallel sides are 15 cm and 13 cm.

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 14

The adjacent sides of a gm AECD measure 34 cm and 20 cm and the diagonal AC is 42 cm long. Find the area of the gm.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 15

The cost of fencing a square lawn at Rs.14 per metre is Rs. 2800. Find the cost of mowing the lawn at Rs.54 per 100 m2.

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 16

Find the area of quad. ABCD in which AB = 42 cm, BC = 21 cm, CD =29 cm, DA = 39 cm and diag. BD = 20 cm.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 17

A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120 m and 44 m. If one of the sides of the gm is 66m long, find its corresponding altitude.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 18

The diagonal of a rhombus are 48 cm and 20cm long. Find the perimeter of the rhombus.

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 19

The adjacent sides of parallelogram are 36 cm and 27 cm in length. If the distance between the shorter sides is 12 cm, find the distance between the longer sides.

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 20

In a four-sided field, the length of the longer diagonal is 128 m. The length of perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 17.3 m. Find the area of the field.

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Chapter 17 – Perimeter and Areas of Plane Figures Exercise MCQ

Question 1

The
length of a rectangular hall is 5 m more than its

breadth. If the area
of the hall is 750 m2 then its length

is

  1. 15
    m
  2. 20
    m
  3. 25
    m
  4. 30
    m
Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 2

The length of a rectangular field is 23 m
more than its breadth. If the perimeter of the field is 206 m, then its area
is

  1. 2420
    m2
  2. 2520
    m2
  3. 2480
    m2
  4. 2620
    m2
Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 3

The length of a rectangular field is 12 m
and the length of its diagonal is 15 m. Then area of the field is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 4

The cost of carpeting a room 15m long
with a carpet 75 cm wide, at Rs.70 per metre,
is Rs. 8400. Then
width of the room is

  1. 9
    m
  2. 8
    m
  3. 6
    m
  4. 12
    m
Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

Question 6

On increasing the length of a rectangle
by 20% and decreasing its breadth by 20%, what is the change in its area?

  1. 20%
    increase
  2. 20%
    decrease
  3. No
    change
  4. 4%
    decrease
Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 7

A
rectangular ground 80 m x 50 m has a path 1 m wide

outside around it. The
area of the path is

  1. 264
    m2
  2. 284
    m2
  3. 400
    m2
  4. 464
    m2
Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 9

The
area of a square field is 6050 m2. The length of its

diagonal
is

  1. 135
    m
  2. 120
    m
  3. 112
    m
  4. 110
    m
Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 10

The area of a square field is 0.5
hectare. The length of its diagonal is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 12

Each
side of an equilateral triangle is 8 cm. Its area is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 15

The base and height of a triangle are in
the ratio 3:4 and its area is 216 cm2. The height of the triangle
is

  1. 18
    cm
  2. 24
    cm
  3. 21
    cm
  4. 28
    cm
Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 16

The lengths of the sides of a triangular
field are 20 m, 21m and 29 m. The cost of cultivating the field at Rs. 9 per m2 is

  1. Rs. 2610
  2. Rs. 3780
  3. Rs. 1890
  4. Rs. 1800
Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 17

The side of a square is equal to the side
of an equilateral triangle. The ratio of their areas is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 18

The side of an equilateral triangle is
equal to the radius of a circle whose area is 154 cm2. The area of
the triangle is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 19

The area of a rhombus is 480 cm2
and the length of one of its diagonals is 20 cm. The length of each side of
the rhombus is

  1. 24
    cm
  2. 30
    cm
  3. 26
    cm
  4. 28
    cm
Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 20

One side of a rhombus is 20 cm long and
one of its diagonals measures 24 cm. The area of the rhombus is

  1. 192
    cm2
  2. 480
    cm2
  3. 240
    cm2
  4. 384
    cm2
Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Chapter 17 – Perimeter and Areas of Plane Figures Exercise Ex. 17B

Question 1

The length of a rectangular park is twice
its breadth and its perimeter is 840 m. Find the area of the park.

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 2

A lawn is in the form of a rectangle
whose sides are in the ratio 5 : 3. The area of the
lawn is 3375 m2. Find the cost of fencing the lawn at Rs. 65 per metre.

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 3

A room is 16 m long and 13.5 m broad.
Find the cost of covering its floor with 0.75-m-wide carpet at Rs. 60 per metre.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 4

The floor of a rectangular hall is 24 m long and 18 m wide. How many carpets, each of length 2.5 m and breadth 80 cm, will be required to cover the floor of the hall?

Solution 4

Area of floor = Length Breadth

                  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of carpet = Length Breadth

                    = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Number of carpets = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                                                          = 216

Hence the number of carpet pieces required = 216

Question 5

A 36 m-long, 15 m-broad verandah is to be paved with stones, each measuring 6 dm by 5 dm. How many stones will be required?

Solution 5

Area of verandah = (36 × 15) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 540 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of stone = (0.6 × 0.5) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures[10 dm = 1 m]

Number of stones required = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, 1800 stones are required to pave the verandah.

Question 6

The area of a rectangle is 192 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresand its perimeter is 56 cm. Find the dimensions of the rectangle.

Solution 6

Perimeter of rectangle = 2(l + b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures2(l + b) = 56 Þ l + b = 28 cm

b = (28 l) cm

Area of rectangle = 192R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

l (28 l) = 192

28l – R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 192

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures– 28l + 192 = 0

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures– 16l 12l + 192 = 0

l(l 16) 12(l 16) = 0

(l 16) (l 12) = 0

l = 16 or l = 12

Therefore, length = 16 cm and breadth = 12 cm

Question 7

A rectangular park 35 m long and 18 m wide is to be covered with grass, leaving 2.5 m uncovered all around it. Find the area to be laid with grass.

Solution 7

Length of the park = 35 m

Breadth of the park = 18 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of the park = (35 18) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 630 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of the park with grass =(35 5) = 30 m

Breadth of the park with grass = (18- 5) m = 13 m

Area of park with grass = (30 13) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 390 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of path without grass = Area of the whole park area of park with grass

                                     = 630 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures– 390 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 240 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, area of the park to be laid with grass = 240 m2

Question 8

A rectangular plot measures 125 m by 78 m. It has a gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at Rs. 75 per R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures.

Solution 8

Length of the plot = 125 m

Breadth of the plot = 78 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of plot ABCD = (125 78) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 9750 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of the plot including the path= (125 + 3 + 3) m = 131 m

Breadth of the plot including the path = (78 + 3 + 3) m = 84 m

Area of plot PQRS including the path

                              = (131 84) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 11004 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of path = Area of plot PQRS Area of plot ABCD

                  = (11004 9750) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                  = 1254 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Cost of gravelling = Rs 75 per m2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresCost of gravelling the whole path = Rs. (1254 75) = Rs. 94050

Hence, cost of gravelling the path = Rs 94050

Question 9

A footpath of uniform width runs all around the inside of a rectangular field 54m long and 35 m wide. If the area of the path is 420 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures, find the width of the path.

Solution 9

Area of rectangular field including the foot path = (54 35) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Let the width of the path be x m

Then, area of rectangle plot excluding the path = (54 2x) (35 2x)

Area of path = (54 35) (54 2x) (35 2x)

                      (54 35) (54 2x) (35 2x) = 420

                      1890 1890 + 108x + 70x – 4R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures = 420

                      178x – 4R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures = 420

                      4R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures – 178x + 420 = 0

                      2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures – 89x + 210 = 0

                      2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures – 84x 5x + 210 = 0

                      2x(x 42) 5(x 42) = 0

                      (x 42) (2x 5) = 0

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 10

The length and the breadth of a rectangular garden are in the ratio 9 : 5. A path 3.5 m wide, running all around inside it has an area of 1911R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures. Find the dimensions of the garden.

Solution 10

Let the length and breadth of a rectangular garden be 9x and 5x.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Then, area of garden = (9x 5x)m = 45R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of park excluding the path = (9x 7) m

Breadth of the park excluding the path = (5x 7) m

Area of the park excluding the path = (9x 7)(5x 7) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresArea of the path = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                            R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures(98x 49) = 1911

     98x = 1911 + 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length = 9x = 9 20 = 180 m

Breadth = 5x = 5 20 = 100 m

Hence, length = 180 m and breadth = 100 m

Question 11

A room 4.9 m long and 3.5 m broad is
covered with carpet, leaving an uncovered margin of 25 cm all around the
room. If the breadth of the carpet is 80 cm, find its cost at Rs.80 per metre.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 12

A carpet is laid on the floor of a room 8m by 5m. There is a border of constant width all around the carpet. If the area of the border is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures, find its width.

Solution 12

Let the width of the carpet = x meter

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of floor ABCD = (8 5) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of floor PQRS without border

= (8 2x)(5 2x)

= 40 16x 10x + R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

= 40 26x + R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of border = Area of floor ABCD Area of floor PQRS

= [40 (40 26x + R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures)] R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

=[40 40 + 26x – R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures] R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

= (26x – R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 13

A 80 m by 64 m rectangular lawn
has two roads, each 5 m wide, running through its middle, one parallel to its
length and the other parallel to its breadth. Find the cost of gravelling the
roads at Rs.40 per m2.

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 14

The dimensions of a room are 14 m x 10 m
x 6.5 m. There are two doors and 4 windows in the room. Each door measures
2.5 m x 1.2 m and each window was of the measure 1.5 m x 1 m. Find the cost
of painting the four walls of the room at Rs.35 per m2.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 15

The cost of painting the four walls of a
room 12 m long at Rs.30 per m2 is Rs.7560 and the cost of covering the floor
with mat at Rs.25 per m2 is Rs.2700. Find the dimensions of the room.

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 16

Find the area and perimeter of a square
plot of land whose diagonal is 24 m long. [R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures]

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 17

Find the length of the diagonal of a square of area 128 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures. Also find the perimeter of the square, correct to two decimal places.

Solution 17

Area of the square = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Let diagonal of square be x

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Length of diagonal = 16 cm

Side of square = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Perimeter of square = [4 side] sq. units

=[ 4 11.31] cm = 45.24 cm

Question 18

The area of a square field is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?

Solution 18

Let d meter be the length of diagonal

Area of square field = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                                 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Time taken to cross the field along the diagonal

                                           R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence, man will take 6 min to cross the field diagonally.

Hence, man will take 6 min to cross the field diagonally.
Question 19

The cost of harvesting a square field at Rs.900 per hectare is Rs.8100. Find the cost of putting a fence
around it at Rs.18 per metre.

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 20

The cost of fencing a square at Rs. 14 per meter is Rs. 28000. Find the cost of mowing the lawn at Rs. 54 per 100 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures.

Solution 20

Rs. 14 is the cost of fencing a length = 1m

Rs. 28000 is the cost of fencing the length= R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Perimeter = 4 side = 2000

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresside = 500 m

Area of a square = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

= 250000 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Cost of mowing the lawn =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 21

In the given figure, ABCD is a
quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 12
cm. Calculate the area of the quadrilateral.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 22

Find the area of the quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29cm, DA = 34 cm and diagonal BD = 20 cm.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 22

Area of quad. ABCD = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABD + Area ofR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC

For area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABD

Let a = 42 cm, b = 34 cm, and c = 20 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

For area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC

a = 29 cm, b = 21 cm, c = 20 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 23

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresACB = 90o and AC = 15 cm.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of quad. ABCD = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC + Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresACD

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Now, we find area of a R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresACD

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of quad. ABCD = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC + Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresACD

                            R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Perimeter of quad. ABCD = AB + BC + CD + AD

                                    =(17 + 8 + 12 + 9) cm

                                    = 46 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresPerimeter of quad. ABCD = 46 cm

Question 24

Find the area of the quadrilateral ABCD in which AD = 24cm, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBAD = 90o and ΔBCD forms an equilateral triangle whose each side is equal to 26 cm. Also find the perimeter of the quadrilateral. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 24

ABCD be the given quadrilateral in which AD = 24 cm, BD = 26 cm, DC = 26 cm and BC = 26 cm

By Pythagoras theorem

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

For area of equilateral R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC, we have

              a = 26 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of quad. ABCD = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABD + Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresDBC

                            = (120 + 292.37) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures= 412.37 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Perimeter ABCD = AD + AB + BC + CD

                       = 24 cm + 10 cm + 26 cm + 26 cm

                       = 86 cm

Question 25

Find the area of a parallelogram with base equal to 25 cm and the corresponding height measuring 16.8 cm.

Solution 25

Area of the ||gm = (base height) sq. unit

= (25 16.8) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 26

The adjacent sides of a parallelogram are 32 cm and 24 cm. If the distance between the longer sides is 17.4 cm, find the distance between the shorter sides.

Solution 26

Longer side = 32 cm, shorter side = 24 cm

Distance between longer sides = 17.4 cm

Let the distance between the shorter sides be x cm

Area of ||gm = (longer side distance between longer sides)

= (shorter side distance between the short sides)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresdistance between the shorter side = 23.2 cm

Question 27

The area of a parallelogram is 392R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures. If its altitude is twice the corresponding base, determine the base and the altitude.

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 28

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Solution 28

Area ofparallelogram = 2 area of DABC

Opposite sides of parallelogram are equal

AD = BC = 20 cm

And AB = DC = 34 cm

In R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresABC we have

a = AC = 42 cm

b = AB = 34 cm

c = BC = 20 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Then, (s a) = 6 cm, (s b) = 14 cm and (s c) = 28 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 29

Find the area of the rhombus, the lengths of whose diagonals are 30 cm and 16 cm. Also find the perimeter of the rhombus.

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

                        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

We know that the diagonals of a rhombus, bisect each other at right angles

OA = OC = 15 cm,

And OB = OD = 8 cm

And R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresAOB = 90

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBy Pythagoras theorem, we have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 30

The perimeter of a rhombus is 60 cm. If one of its diagonals is 18 cm long find (i) the length of the other diagonal and (ii) the area of the rhombus.

Solution 30

(i)Perimeter of rhombus = 4 side

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures4 side = 60 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

By Pythagoras theorem

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

OB = 12 cm

OB = OD = 12 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBD = OB + OD = 12 cm + 12 cm = 24 cm

                       Length of second diagonal is 24 cm

 

(ii) Area of rhombus = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 31

The area of a rhombus is 480R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures and one of its diagonals measures 48 cm. Find (i) the length of the other diagonals, (ii) the length of each of its sides, and (iii) its perimeter.

Solution 31

(i)Area of rhombus = 480 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

One of its diagonals = 48 cm

Let the second diagonal =x cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Hence the length of second diagonal 20 cm

(ii)We know that the diagonals of a rhombus bisect each other at right angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresAC = 48, BD = 20 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresOA = OC = 24 cm and OB = OD = 10 cm

By Pythagoras theorem , we have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

(iii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresPerimeter of the rhombus = (4 26) cm = 104 cm

Question 32

The parallel sides of a trapezium are 12
cm and 9 cm and the distance between them is 8 cm. Find the area of the
trapezium.

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 33

The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures, find the depth of the canal.

Solution 33

Areaof cross section = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Question 34

Find the area of a trapezium whose parallel sides are 11 m and 25 m long, and the non parallel sides are 15 m and 13 m long.

Solution 34

Let ABCD be a given trapezium in which

AB = 25, CD = 11

BC = 15, AD = 13

Draw CE || AD

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

In ||gm ADCE, AD || CE and AE || CD

AE = CD = 11 cm,

And BE = AB BE

           = 25 11 = 14 cm

In R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBEC,R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBEC = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

Let height of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBEC is h

Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane FiguresBEC = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

From (1) and (2), we get

7h = 84 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figuresh = 12 m

Area of trapezium ABCD

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Perimeter And Areas Of Plane Figures

 

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