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Area of a parallelogram

A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel.

The area of a parallelogram can be found by cutting off a triangle at one end and adding it to the other end to form a rectangle as shown here. The area of the figure has, of course, not changed.

area of a parallelogram_1

So area of a parallelogram  =  area of a rectangle  =  bh

Let us look at a few examples of finding the area of a parallelogram.


area of a parallelogram_2Example 1 : Find the area of this parallelogram.

Area of a parallelogram = bh

=  9 x 6

=  54 cm2


Example 2 : Find the area of the parallelogram by translating a right-angled triangle and forming a rectangle.

area of a parallelogram_3

Area of parallelogram = bh

=  10 x 4

=  40 cm2


area of a parallelogram_4Example 3 : What is the area of this shape?

This shape is comprised of a rectangle and a parallelogram.

Area of rectangle  =  lb

=  8 x 3

=  24 cm2

Area of parallelogram  =  bh

=  8 x 4

=  32 cm2

Area of shape  =  area of rectangle  +  area of parallelogram

=  24 + 32

=  56 cm2