# The Area of a Parallelogram

A parallelogram is a quadrilateral whose opposite sides are of equal length and parallel. The diagonals of a parallelogram are unequal and bisect each other. If is a parallelogram, then its area can be calculated in two ways.

**(a) When the base and height are given:**

Since is a parallelogram with base and height,

the area of the parallelogram the area of the rectangle .

The area of the parallelogram .

The area of the parallelogram (as ).

The area of the parallelogram .

the area of the parallelogram base height.

**(b) When the adjacent sides and their included angle is given:**

Since is a parallelogram, take and as its two adjacent sides with the included angle .

the area of the parallelogram

But

Or

Or .

the area of

the area of the parallelogram the product of the adjacent sides

__Example__:

Find the base of a parallelogram whose area is square cm and height cm.

__Solution__:

Since the area square cm

The height cm

the area of the parallelogram base height.

base .

The base cm.

__Example__:

Find the area of a parallelogram, two adjacent sides of which are cm and cm and their included angle is.

__Solution__:

Here, one side cm, the other side cm, and

the area

square cm.