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Example 12: In the adjoining figure, area of the parallelogram is 24 cm , and the base of the
parallelogram is 3 cm. Find the height of the parallelogram.

Solution: In the adjoining figure,
h
let the height of the parallelogram be h. 3 cm

Base of the parallelogram, b = 3 cm,
We have, area of parallelogram = b × h

2
2
Therefore, 3 cm × h = 24 cm (Given, area of the parallelogram = 24 cm )
24
\ h = cm = 8 cm
3
Thus, the height of the parallelogram corresponding to base is 8 cm.

Example 13: A side of a parallelogram measuring 12 cm is at a perpendicular distance of 15 cm
from its opposite side. Find the area of the parallelogram.
D C
Solution: Base of the parallelogram, b = 12 cm,

Height of the parallelogram, h = 15 cm
15 cm
We have, area of the parallelogram = base × height

= (12 × 15) cm 2 A 12 cm B
= 180 cm 2

2
So, the area of the parallelogram is 180 cm .
2
Example 14: Find the height ‘h’ if the area of the parallelogram is 48 cm and
the base is 4 cm.

Solution: Let height of the parallelogram be h cm, and h

base of the parallelogram, b = 4 cm.
We have, area of the parallelogram = base × height 4 cm

2
2
48 cm = 4 cm × h [Area of the parallelogram = 48 cm , given]
h = 48 cm = 12 cm
4
Thus, the height of the parallelogram is 12 cm.

Example 15: The two sides of the given parallelogram are 8 cm and 6 cm. The height corresponding
to the base CD is 3 cm. Find the (a) area of the parallelogram. (b) the height corresponding to the
base AD. B
A
Solution: In the given figure,

(a) Base of the parallelogram, b = 8 cm h 3 cm
6 cm
Height of the parallelogram, h = 3 cm

We have, Area of parallelogram = b × h
D 8 cm C
= 8 cm × 3 cm = 24 cm 2

289 Perimeter and Area