Area of a Parallelogram

formula

Area of parallelogram = base x height

Area of the parallelogram:

To get the area of the parallelogram, we first draw a perpendicular line segment from one corner of the parallelogram to the opposite side. This is the height (h) of the parallelogram. The area of a parallelogram is equal to the product of its length and height.

Area of a parallelogram = base x height

You may notice that lh is also the area of a rectangle with dimensions l and h. The diagram below will explain why. If we cut out the triangle ABC and add it to the other side (triangle DEF), you will have a rectangle with dimensions l and h that has the same area as the original parallelogram.

Area of parallelogram ABCD = (base x height)

• Any side of a parallelogram can be chosen as the base of the parallelogram.

• The perpendicular dropped on that side from the opposite vertex is known as height (altitude).

Example

Find the height ‘x’ if the area of the parallelogram is 24 cm2 and the base is 4 cm.

Area of parallelogram = b × h

Therefore, 24 = 4 × x

24/4 = x

x = 6 cm

So, the height of the parallelogram is 6 cm.

Example

The two sides of the parallelogram ABCD are 6 cm and 4 cm. The height corresponding to the base CD is 3 cm.
Find the
(i) area of the parallelogram.
(ii) the height corresponding to the base AD.

(i) Area of parallelogram = b × h
= 6 cm × 3 cm = 18 cm2

(ii) base (b) = 4 cm, height = x (say), Area = 18 cm2

Area of parallelogram = b × x

18 = 4 × x

18/4 = x

Therefore, x = 4.5 cm

Thus, the height corresponding to base AD is 4.5 cm.

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