# KC Sinha Mathematics Solution Class 9 Chapter 14 Areas (Herons formula) exercise 14.2

Page 14.29

### EXERCISE 14.2

Type 1

#### QUESTION 1

The base and height of a parallelogram are in the ratio of 3:2 and area is 600 sq. metres . Find its base and height

Sol :

#### QUESTION 2

The area of a parallelogram is 72cm2 . If its one perpendicular (altitude) is double of the corresponding base , find the base and altitude .

Sol :

#### QUESTION 3

Two adjacent sides of a parallelogram ABCD are 5cm and 3.5cm and length of its diagonal is 6.5cm . Find the area of the parallelogram

Sol :

#### QUESTION 4

Two adjacent sides of a field which in the shape of a parallelogram are 25m and 39m and one diagonals is 56m , then what will be the cost of laying stone in the field at Rs 3.50 per sq. metre ?

Sol :

#### QUESTION 5

Area of a parallelogram ABCD is 120cm2 . If AB=15cm , then find the distance between AB and DC . If ∠CDA=150° , find the perimeter of the parallelogram

<fig >

<hint>

Sol :

TYPE 2

#### QUESTION 6

Each side of a rhombus is 10m and its one diagonal is 16m , find the area of the rhombus

Sol :

#### QUESTION 7

The diagonals of a rhombus are 7m and 24m , then find its

(i) area

(ii) side

(iii) perimeter

(iv) height

Sol :

#### QUESTION 8

Perimeter of a rhombus is 20cm and its diagonal is 8cm . Find the area of the rhombus and length of other diagonal

Sol :

#### QUESTION 9

In figure , (i) OPQR is a rhombus of which three vertices lie on a circle with center O . If area of rhombus be 32√3cm2 , then find the radius of the circle

<fig>

<hint>

Sol :

#### QUESTION 10

OABC is a rhombus whose three vertices lie on the circle with centre O . If radius if the circle be 10cm , then find the area of the rhombus

[Hint: Proceed as in question 9]

Sol :

#### QUESTION 11

The cross section of canal is trapezium. If width of the upper side is 10m and that of base is 6cm and cross section area of the canal is 72m, find its depth

<hint>

Sol :

#### QUESTION 12

Area of a trapezium is 210m2 . If perpendicular distance between the parallel sides is 15m and one of thses parallel sides is 12m , then find its other parallel side

Sol :

#### QUESTION 13

The parallel sides of a trapezium are 18 cm and 10 cm. If each of the order two sides is 5cm , then find its area

Sol :

#### QUESTION 14

A trapezium PBCQ whose parallel sides QC and PB are in the ratio 7:5 , has been cut from a rectangle ABCD as shown in figure (i) If area of the trapezium is 4/7 of the area of the rectangle  ,then find the length of sides QC and PB

<fig>

<hint>

Sol :

#### QUESTION 15

Parallel sides of a trapezium are 46 m and 25m and two other sides are 20m and 13m . Find the area of the trapezium

<fig>

<hint>

Sol :

TYPE 4

#### QUESTION 16

ABCD is a quadrilateral whose diagonal AC=15cm and lengths of perpendiculars drawn from opposite vectors are 3cm and 5cm . Find the area of the quadrilateral

Sol :

#### QUESTION 17

The diagonal of a quadrilateral is 50cm and perpendicular drawn to it from opposite vertices are 10cm and 20cm . Find the area of the quadrilateral .

Sol :

#### QUESTION 18

Area of a f‌ield in the shape of a quadrilateral is 486m2 and its one diagonal is 36m . Perpendiculars drawn from opposite vertices on this diagonal are in the ratio of 4:5 . Find the lengths of the perpendiculars

<hint>

Sol :

#### QUESTION 19

Find the area if quadrilateral ABCD whose sides are 5m , 12m , 15m and 14m and angle between first two sides is 90°

Sol :

#### QUESTION 20

Find the area of quadrilateral ABCD in which

(i) AB=7cm , BC=12cm , CD=12.6cm , DA=9cm and diagonals AC=15cm

(ii) AB=3cm , BC=4cm , CD=6cm , DA=5cm and diagonal AC=5cm

Sol :

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