EXERCISE 11.2
Page No 216:
Question 1:
Find the area of each of the following parallelograms:
Answer:
Area of parallelogram = Base × Height
(a) Height= 4 cm
Base = 7 cm
Area of parallelogram = 7 × 4 = 28 cm^{2}
(b) Height= 3 cm
Base = 5 cm
Area of parallelogram = 5 × 3 = 15 cm^{2}
(c) Height= 3.5 cm
Base = 2.5 cm
Area of parallelogram = 2.5 × 3.5 = 8.75 cm^{2}
(d) Height= 4.8 cm
Base = 5 cm
Area of parallelogram = 5 × 4.8 = 24 cm^{2}
(e) Height= 4.4 cm
Base = 2 cm
Area of parallelogram = 2 × 4.4 = 8.8 cm^{2}
Question 2:
Find the area of each of the following triangles:
Answer:
(a) Base = 4 cm, height= 3 cm
Area = 6 cm^{2}
(b) Base = 5 cm, height= 3.2 cm
Area = 8 cm^{2}
(c) Base = 4 cm, height= 3 cm
Area = 6 cm^{2}
(d)Base = 3 cm, height= 2 cm
Area = = 3 cm^{2}
Question 3:
Find the missing values:
So No |
Base |
Height |
Area of parallelogram |
a. |
20 cm |
– |
246 cm^{2} |
b. |
– |
15 cm |
154.5 cm^{2} |
c. |
– |
8.4 cm |
48.72 cm^{2} |
d. |
15.6 cm |
– |
16.38 cm^{2} |
Answer:
Area of parallelogram = Base × Height
(a) b = 20 cm
h = ?
Area = 246 cm^{2}
20 × h = 246
Therefore, the height of such parallelogram is 12.3 cm.
(b) b = ?
h = 15 cm
Area = 154.5 cm^{2}
b × 15 = 154.5
b = 10.3 cm
Therefore, the base of such parallelogram is 10.3 cm.
(c) b = ?
h = 8.4 cm
Area = 48.72 cm^{2}
b × 8.4 = 48.72
Therefore, the base of such parallelogram is 5.8 cm.
(d) b = 15.6 cm
h = ?
Area = 16.38 cm^{2}
15.6 × h = 16.38
Therefore, the height of such parallelogram is 1.05 cm.
Page No 217:
Question 4:
Find the missing values:
Base |
Height |
Area of triangle |
15 cm |
_______ |
87 cm^{2} |
_______ |
31.4 mm |
1256 mm^{2} |
22 cm |
_______ |
170.5 cm^{2} |
Answer:
(a) b = 15 cm
h = ?
Area =
Therefore, the height of such triangle is 11.6 cm.
(b) b = ?
h = 31.4 mm
Area =
Therefore, the base of such triangle is 80 mm.
(c) b = 22 cm
h = ?
Area =
Therefore, the height of such triangle is 15.5 cm.
Question 5:
PQRS is a parallelogram (see the given figure). QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find:
(a) the area of the parallelogram PQRS
(b) QN, if PS = 8 cm
Answer:
(a) Area of parallelogram = Base × Height = SR × QM
= 7.6 × 12 = 91.2 cm^{2}
(b) Area of parallelogram = Base × Height = PS × QN = 91.2 cm^{2}
QN × 8 = 91.2
Question 6:
DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD (see the given figure). If the area of the parallelogram is 1470 cm^{2}, AB = 35 cm and AD = 49 cm, find the length of BM and DL.
Answer:
Area of parallelogram = Base × Height = AB × DL
1470 = 35 × DL
Also, 1470 = AD × BM
1470 = 49 × BM
Question 7:
ΔABC is right angled at A (see the given figure). AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ΔABC. Also find the length of AD.
Answer:
Area == 30 cm^{2}
Question 8:
ΔABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm (see the given figure). The height AD from A to BC, is 6 cm. Find the area of ΔABC. What will be the height from C to AB i.e., CE?
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