# Area of rhombus formula explained with example

Learn and know what is the area of rhombus formula? In mensuration. In mathematics, mensuartion is a one of the chapters, where we will learn only formulas related to polygons. For example, Area of rectangle, area of square, area of parallelogram and so on. Before learning the formula for area of rhombus, we will learn what is rhombus? And how to explain it. Also we will list out properties. All these properties we need to remember because they will help us in solving problems which are based on rhombus.

## What is rhombus in math?

A quadrilateral is called as a rhombus “if the adjacent sides are equal and also the opposite sides are parallel and no angle is equal to the ${ 90 }^{ 0 }$.

Properties:

Diagonals are not equal.

All the four sides are equal in dimensions same as square.

The two diagonals of a rhombus are bisecting each other.

The opposite sides are always equal in rhombus and also they are parallel.

The two diagonals intersect at ${ 90 }^{ 0 }$.

### The formula for area of rhombus as follows:

We know that any quadrilaterals will be having 2 diagonals. Why am pointing out diagonals here? Because there is some relation among diagonals and area of rhombus formula. Half of the product of the diagonals gives the area of rhombus. That is area of rhombus formula = $\frac { 1 }{ 2 }$ x product of diagonals (${ d }_{ 1 }$ x ${ d }_{ 2 }$) = $\frac { 1 }{ 2 }$ x (${ d }_{ 1 }$ x ${ d }_{ 2 }$)

Examples:

The 2 diagonals of a rhombus are given as 3 cm and 5 cm then what is its area?

Solution:

The product of 2 diagonals is i.e. 3 x 5 = 15 ${ cm }^{ 2 }$. Therefore the area of rhombus is equal to $\frac { 1 }{ 2 }$ x 15 = 7.5 ${ cm }^{ 2 }$.

The area of rhombus is given as the 28 ${ m }^{ 2 }$ and one of the two diagonals is given as 8m then what is its second diagonal?

Solution:

According to area of rhombus formula,

28 = $\frac { 1 }{ 2 }$ x 8 x ${ d }_{ 2 }$

28 x 2 = 8 x ${ d }_{ 2 }$

$\frac { 56 }{ 8 }$ = ${ d }_{ 2 }$

7 = ${ d }_{ 2 }$

Therefore, the second diagonal of rhombus is 7m. 