How to Find Area of Rhombus

The area of the rhombus can be calculated by three different methods by using diagonal, using base and height, and using trigonometry.

These are the three important methods for finding area of Rhombus:

1. Area of Rhombus when Diagonals are given
2. Area of Rhombus using Base and Height
3. Area of Rhombus using Trigonometric Ratios

Let’s discuss all these methods in detail.

Area of Rhombus with Diagonals 

Area = (d₁ × d₂)/2 sq. units

Where,

d₁ is the length of diagonal 1

d₂  is the length of diagonal 2

Let’s try to understand this formula with the help of an example.

Example 1: Find the area of a rhombus having diagonals 16 m and 18 m.

Solution:

Diagonal 1, d₁ = 16 m

Diagonal 2, d₂ = 18 m

Area of a rhombus, A = (d₁ × d₂) / 2

= (16 × 18) / 2

= 288 / 2

= 144 m²

Thus, the area of the rhombus is 144 m²

Area of Rhombus using Base and Height

Area of a Rhombus = b × h sq units

Where,

b is the length of any side of the rhombus

h is the height of the rhombus

Example 2: Find the area of a rhombus having base of 12 m and height is 16 m.

Solution:

Base, b = 12 m

Height, h = 16 m

Area, A = b × h

            = 12 × 16 m²

         A = 192 m²

Thus, the area of the rhombus is 192 m²

Area of Rhombus using Trigonometric Ratios

Area of a Rhombus = b² × sin(A) sq. units

Where,

b is the length of any side of the rhombus

A is a measure of any interior angle

Example 3: Find the area of a rhombus if the length of its side is 12 m and one of its angles A is 60°

Solution:

Side = s = 12 m

Angle A = 60°

Area = s² × sin (60°)

A = 144 × √3/2

A = 72√3 m²

Rhombus is a parallelogram in which all four sides are equal and opposite pairs of lines are congruent. The opposite angles in a rhombus are equal. The area of Rhombus is the total space occupied a Rhombus in a 2d Plane.

It is a special type of parallelogram in which all sides are equal to each other. The internal angle of Rhombus is not mandatory to be right angle.

Let’s learn more about area of Rhombus formula, derivation and examples in detail.