# Area of a Parallelogram

A parallelogram is a quadrilateral whose opposite sides are 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,

Area of the parallelogram Area of the rectangle

Area of the parallelogram

Area of the parallelogram (as )

Area of the parallelogram

Area of parallelogram base height

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

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

Area of parallelogram

But

Or

Or

Area of

Area of Parallelogram Product of adjacent sides

__Example__:

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

__Solution__:

** **Since, area square cm

height cm

Area of parallelogram base height

base

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, other side, cm,

Area

square cm