Area of 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, the rhombus is formed.

Let ABCD be a rhombus then its area can be evaluated in two ways:

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

Let one side be equal to a with include angle \theta . Since, the diagonal AC divides the rhombus into two equal triangle, therefore


Area of the rhombus  = 2 \times {\text{area of  }}\Delta ABC
Area of the rhombus  = 2\left( {\frac{1}{2}a  \times a \times \sin \theta } \right) = 2\left( {\frac{1}{2}{a^2}} \right)\sin  \theta  = {a^2}\sin \theta
Area of the rhombus  = {({\text{one  side}})^2}\sin \theta

(2) When two diagonal are given:

Let d and d' be the length of the diagonal AC and BD respectively and since, the rhombus is divided into four equal triangles, therefore


Area of the rhombus  = 4 \times \frac{1}{2}  \times \frac{{BD}}{2} \times \frac{{CA}}{2} = 4 \times \frac{{BD \times CA}}{8}  = \frac{{BD \times CA}}{2}

Area of the rhombus  = \frac{{AC \times  BD}}{2} = \frac{{d \times d'}}{2}

Area of the rhombus  = \frac{{{\text{Product  of two diagonals}}}}{2}


The length of each side of a rhombus is 120cm and two of its opposite angles are 60^\circ each. Find the area.


Given that each side, a = 120 and \theta  = 60^\circ
Area of the rhombus  = {({\text{side}})^2}  \times \sin \theta
Area of the rhombus  = 120 \times 120 \times  \sin 60^\circ  = 120 \times 120 \times  0.866 = 12470.4 square cm


The diagonal of a rhombus are 40m and 30m. Find its area.



Given that diagonal are d = 40m and d' = 30m

Area of the rhombus  = \frac{{d \times d'}}{2}  = \frac{{40 \times 30}}{2} = 600 Square m