# The Area of a Rhombus

A rhombus is a quadrilateral having all sides with unequal diagonals which bisect each other.

** Note: **If a square is pressed from two opposite corners, a rhombus is formed.

Let be a rhombus, then its area can be evaluated in two ways.

**(1) When one side and the included angle is given:**

Let one side be equal to with includes angle . Since the diagonal divides the rhombus into two equal triangles, therefore

The area of the rhombus .

The area of the rhombus .

The area of the rhombus .

**(2) When two diagonal are given:**

Let and be the length of the diagonals and respectively, and since the rhombus is divided into four equal triangles, therefore

The area of the rhombus .

The area of the rhombus .

The area of the rhombus .

__Example__:

The length of each side of a rhombus is cm and two of its opposite angles are each. Find the area.

__Solution__:

Given that each side and ,

the area of the rhombus .

The area of the rhombus square cm.

__Example__:

The diagonals of a rhombus are m and m. Find its area.

__Solution__:

Given that the diagonals are m and m,

the area of the rhombus square m.