A **Rhombus** is a type of quadrilateral. It is a special case of a **parallelogram**, with its **diagonals intersecting each other at 90 degrees**.

It 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

**Angles in Rhombus**

- Its shape has four interior angles.
- The interior angles of a rhombus sum up to \(360^\circ\).
- Opposite pair of angles are equal to each other.
- The adjacent angles are supplementary.
- Diagonals bisect each other at right angles or \(90^\circ\).
- The diagonals bisect all the four angles.

**Perimeter of Rhombus**

The total length of its boundaries gives the perimeter of a shape. That is the sum of all its four given sides,

The perimeter is given by \(P = 4a\), here \(P\) is the perimeter, and \(a\) is the length of each side.

**Area of 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 its area & \(d_1\), and \(d_2\) are its diagonals.

**Altitude of Rhombus**

The height or the perpendicular distance from one of the sides from chosen base to the opposite side is the altitude. And, it is given as,

Altitude, \(H = \frac{Area}{Base}\)

**Properties of a Rhombus**

- All sides are equal.
- Opposite sides are parallel to each other.
- Opposite angles are equal to each other.
- Diagonals bisect each other.
- The Sum of adjacent angles is \(180^circ\).
- Diagonals bisect the angles at the corner.
- It is a special case of a parallelogram, with diagonals bisecting each other at \(90^\circ\).

**Solved Examples**

**Question 1.** Find the are of a rhombus with diagonals \(d_1 = 4cm\) & \(d_2 = 10cm\).

**Solution.** The area of a rhombus is,

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

\(A = \frac{1}{2} 4 \cdot 10\)

\(A = 20 {cm}^2\)

**Question 2.** Find the diagonal of a rhombus if its area is 1331 cm^{2} and length measure of longest diagonal is 22 cm.

**Solution.** Area can be given as,

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

\(1331 = \frac{1}{2}(22 \cdot d)\)

\(2662 = 22 \cdot d\)

or, \(d = 121cm\).

Therefore, the Length of another diagonal is 121 cm.

**FAQs**

**What is rhombus?**It is a special case of a parallelogram, with its diagonals intersecting each other at 90 degrees.

**What is the area of a rhombus?**It 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 & \(d_1\), and \(d_2\) are its diagonals.

**Do diagonals of a rhombus bisect each other?**Yes, they bisect each other at \(90^\circ\).

**Can a rhombus be a square?**It can be a square if all four corner angles are \(90^\circ\).