The area of a rhombus is the product of the length of the base and its height. A rhombus is a parallelogram with all sides being equal. The adjacent angles of a rhombus added up to 180°. The opposite sides of a rhombus are equal. The diagonals of a rhombus bisect each other at right angles. The diagonals of a rhombus are the line of symmetry. On this page, we will discuss the area of a rhombus in detail.

## What is the area of a rhombus?

The area of a rhombus is the product of the length of the base and its height. Or the area of a rhombus is half the product of the diagonals. i.e area of rhombus = 1/2 × the product of the diagonals.

## How to find the area of a rhombus

To find the area of a rhombus follows these simple steps:

• make sure the unit of measurement of the lengths of rhombus are the same.

• multiply the lengths of the diagonals

• multiply the product of the diagonals by half i.e 1/2 × the product of diagonals.

• simplify to get the area of the rhombus.

Lets us understand better by working through some examples.

Example 1: The diagonals of a rhombus are 7cm and 11cm long. Find the area of the rhombus.

Solution

The Area of a rhombus is

\begin{aligned}&= \frac{1}{2} × \text{the product of diagonals}\\ &= \frac{1}{2} × (7cm × 11cm)\\ &= \frac{1}{2} × (77cm^2)\\ &= 38.5cm^2\end{aligned}

This is pretty good, right? Let’s look at another example

Example 2: find the area of the rhombus below

Solution

The area of a rhombus is

\begin{aligned}&= \frac{1}{2} × \text{the product of diagonals}\\ \text{since the lengths of the diagonals are 5m+5m = 10m and 6m+6m = 12m}\\ &= \frac{1}{2} × (10m × 12m)\\ &= \frac{1}{2} × (120m^2)\\ &= 60m^2 \end{aligned}

Example 3: The side of the rhombus is half the longer diagonal. The height of the rhombus is 3m and the area of the rhombus is 21 m². Find the length of the longer diagonal of the rhombus.

Solution

Let x represent the longer diagonal of the rhombus, one side of the rhombus is = 1/2 of the longer diagonal = 1/2x, the height of the rhombus is = 3m, and the area of the rhombus is = 21m² as shown in the diagram below.

Since the area of a rhombus is = length of base × height, where b= 1/2x, h = 3, and area = 21m².

Therefore, the area of the rhombus is

\begin{aligned}&\text{area} \space = \frac{1}{2}xm × 3m\\ &21m^2 = \frac{1}{2}xm × (3m)\\ &21= \frac{3x}{2}\\ &42= 3x, \space \text{divide both sides by 3}\\ &\frac{42}{3}=\frac{3x}{3}\\ &14=x\end{aligned}

Therefore, the length of the longer diagonal of the rhombus is 14m.

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