A rhombus is a type of quadrilateral. It is a special case of a **parallelogram**, with its **diagonals intersecting each other at 90 degrees**. The area of the rhombus is calculated by taking the **product of its diagonals and dividing it by 2**.

The rhombus is an **equilateral quadrilateral**; all of its sides are equal in length, hence the term ‘rhombus’, which has been derived from the ancient Greek word* ‘rhombos’*, which means something that spins.

Index

**Area of a Rhombus**

The area of the rhombus is calculated by taking the product of its diagonals and dividing it by 2,

\(A = \frac{1}{2} d_1 \cdot d_2\),

Here, \(A\) is the area of the rhombus & \(d_1\), and \(d_2\) are its diagonals.

Let ABCD be a Rhombus

E being the center and AC and BD as diagonals.

The \(A\) can be written as:

\(A = 4 \cdot\) Area of \(\triangle AEB\)

\(A = 4 \cdot \frac{1}{2} (AE)(BE)\)

(Since, diagonals perpendicularly bisect each other in a rhombus.)

\(\begin{align}

A & = 4 \cdot \frac{1}{2} (\frac{1}{2} AC) (\frac{1}{2} BD)\\

& = 4 \cdot \frac{1}{8} AC \cdot BD\\

& = \frac{1}{2} AC \cdot BD\\

\end{align}

\)

Let \(AC = d_1\) & \(BD = d_2\)

Then, we can rewrite it as,

\(A = \frac{1}{2} d_1 \cdot d_2\)

**Solved Examples**

**Question 1.** Find the area of rhombus with the diagonals being 5cm and 10cm.

**Solution.** Area of a rhombus can be given as,

\begin{align}

A & = \frac{1}{2} d_1 \cdot d_2\\

& = \frac{1}{2} 5 \cdot 10\\

& = 5 \cdot 5 = 25cm^2\\

\end{align}

\)

**Question 2.** Find the rhombus ABCD, with center O. If the area of its triangle AOB, formed by the diagonals, is 7 cm^{2}.

**Solution.**

Area of rhombus ABCD = Area of \(\triangle AOB\) + Area of \(\triangle BOC\) + Area of \(\triangle COD\) + Area of \(\triangle AOD\)

\(\begin{align}

\text{Area of rhombus ABCD} & = 4 \cdot \text{Area of } \triangle AOB\\

& = 4 \cdot 7 = 28cm^2\\

\end{align}

\)

**FAQs**

**What is the area of the Rhombus?**The formula of area of Rhombus is

\(A = \frac{1}{2} d_1 \cdot d_2\)

Here, \(d_1\) and \(d_2\) are the two diagonals to the rhombus.

**What is the perimeter of the Rhombus?**The formula gives the perimeter of the rhombus

\(P = 4a\), where \(a\) is the length of a side.

**Do diagonals bisect each other in Rhombus?**Diagonals of the Rhombus bisect each other at \(90^\circ\).

**Are the diagonals of the rhombus equal?**Diagonals of a rhombus may or may not be equal.