In this blog, we will learn how to find the area and perimeter of a parallelogram.

What is a parallelogram?

A parallelogram has two pairs of parallel and equal sides. In the given parallelogram PQRS, PQ and RS are parallel and equal and sides PS and QR are parallel and equal.

Parallelogram:

PQ = RS, PQ || RS and

PS = QR, PS || QR

Let us find the area of a parallelogram. Here ABCD is a parallelogram in which the length of CD is L and the distance between these parallel sides is h. If we cut the triangle from the left of the parallelogram and join at the right, we get a rectangle whose sides are L and h and we know that area of a rectangle is length into breadth. So, the area of a given parallelogram is given by base into the perpendicular distance between the parallel sides.

Area of Parallelogram:

Area of Parallelogram = Side x Perpendicular Height between parallel sides = l x h

We can find the area in another way. If the length of the side and perpendicular distance are given as in the figure. Then we can cut the lower triangle from the parallelogram and join in the upper region of the parallelogram, we again get a rectangle of sides b and h. So, the area of the given parallelogram is given by side b into h.

Area of Parallelogram:

Area of Parallelogram = Side x Perpendicular Height between parallel sides =�b x h

Now, let us study the perimeter of a parallelogram. The perimeter of any geometrical shape is the distance around the outside of the shape. So, the perimeter of the given parallelogram ABCD is the sum of sides AB, BC, CD and DA which is equal to 2(a + b)

The Perimeter of a Parallelogram:

Perimeter of parallelogram = sum of all four sides = 2(a + b)

Let us take an example to find the area of the parallelogram.�

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

Solution: In parallelogram ABCD, 

Base = 4 cm, 

perpendicular height = x cm and

Area of parallelogram = 24 cm²

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