Here we will discuss about how to find the area of a parallelogram. To calculate area of parallelogram we need to remember the formula and solve step-by-step.
ABCD is a parallelogram with base (b) and altitude (h).
Area of parallelogram = 2 × Area of ∆ABC
= 2 × 1/2 × base × height sq. units
= 2 × 1/2 × AB × CE sq. units
= b × h sq. units
= base × height sq. unit
Perimeter of parallelogram = 2(AB + BC)
= 2 × (Sum of adjacent sides)
Examples
1. The base of the parallelogram is thrice its height. If the area is 192 cm², find the base and height.
Solution:
Let the height of the parallelogram = x cm
then the base of the parallelogram = 3x cm
Area of the parallelogram = 192 cm²
Area of parallelogram = base × height
192 = 3x × x
⇒ 3x² = 192
⇒ x² = 64
⇒ x = 8
Therefore, 3x = 3 × 8 = 24
Therefore, Base of the parallelogram is 24 cm and height is 8 cm.
2. A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.
Solution:
Adjacent sides of parallelogram = 2 cm and 9 cm
Distance between shorter sides = 8 cm
Area of parallelogram = b × h
= 9 × 8 cm²
= 72 cm²
Again, area of parallelogram = b × h
⇒ 72 = 12 × h
⇒ h = 72/12
⇒ h = 6 cm
Therefore, the distance between its longer side = 6 cm.
4. Find the area of the parallelogram with a base of 4 cm and height of 5 cm.
Solution:
Given:
Base, b = 4 cm
h = 5 cm
We know that,
Area of Parallelogram = b × h Square units
= 4 × 5 = 20 sq.cm
Therefore, the area of a parallelogram = 20 cm2
5. Find the area of a parallelogram whose breadth is 8 cm and height is 11 cm.
Solution:
Given,
b = 8 cm
h = 11 cm
Area of a parallelogram
= b × h
= 8 × 11 cm2
= 88 cm2
6. The base of the parallelogram is thrice its height. If the area is 192 cm2, find the base and height.
Solution:
Let the height of the parallelogram = h cm
then, the base of the parallelogram = 3h cm
Area of the parallelogram = 192 cm2
Area of parallelogram = base × height
Therefore, 192 = 3h × h
⇒ 3 × h2 = 192
⇒ h2 = 64
⇒ h = 8 cm
Hence, the height of the parallelogram is 8 cm, and breadth is
3 × h
= 3 × 8
= 24 cm
7. The area of a parallelogram is 500 sq.cm. Its height is twice its base. Find the height and base.
Solution:
Given, area = 500 sq.cm.
Height = Twice of base
h = 2b
By the formula, we know,
Area = b x h
500 = b x 2b
2b2 = 500
b2 = 250
b = 15.8 cm
Hence, height = 2 x b = 31.6 cm