Area of Rhombus Formulas | List of Area of Rhombus Formulas You Should Know - BYJUS

# Area of Rhombus Formulas

The quantity of region that a rhombus encloses in a two-dimensional plane is known as the area of the rhombus. A rhombus is a type of quadrilateral with four congruent sides. We will study the formula used to find the area of a rhombus in addition to observing a few solved examples....Read MoreRead Less

### Introduction

A rhombus is a type of a parallelogram in which all the sides are congruent. This implies that a rhombus has four equal sides. The major distinction between a square and a rhombus is that each interior angle of the square is a right angle, but this is not the case in a rhombus.

As we already know, the region enclosed by a rhombus in a two-dimensional plane is known as the area of the rhombus.

A rhombus is defined by the following attributes.

• All of the sides of a rhombus are equal in length, making it an equilateral quadrilateral
• Diagonals in a rhombus intersect each other at right angles
• The diagonals are the angle bisectors in a rhombus

### Formula for the Area of a Rhombus

The area of a rhombus is half the product of the lengths of the diagonals. Depending on the characteristics we are aware of, various formulas can be employed to determine the area of a rhombus. These formulas are:

• Using the base and height,

A = b $$\times$$ h

• Using the diagonal length,

A = $$\frac{1}{2}\times d_1\times d_2$$

• Using trigonometry,

A = $$b^2 \times sin(a)$$

Where,

A = Area of rhombus

$$d_1$$ = Length of the first diagonal

$$d_2$$ = Length of the second diagonal

b = Side length

h = Height of the rhombus

a = Measure of any interior angle

### Solved Examples

Example 1: Determine the area of a rhombus with diagonals measuring 8 cm and 10 cm.

Solution:

Data stated in the question,

First diagonal, $$d_1$$ = 8 cm

Second diagonal, $$d_2$$ = 10 cm

A = $$\frac{d_1\times d_2}{2}$$ Write the formula for the area of a rhombus

= $$\frac{8\times 10}{2}$$  Substitute the values

= $$\frac{80}{2}$$     Multiply

= 40     Divide

Hence, the area of the rhombus is 40 square centimeters.

Example 2: Determine the length of the second diagonal if the area of a rhombus is 168 square inches and the length of one of its diagonals is 21 inches.

Solution:

The data provided in the question,

First diagonal, $$d_1$$ = 21 in

Area of rhombus, A = 168 $$\text{in}^2$$

A = $$\frac{d_1\times d_2}{2}$$       Write the formula for the area of a rhombus

168 = $$\frac{21\times d_2}{2}$$       Substitute the values

168 $$\times$$ 2 = 21 $$\times~d_2$$   Multiply each side by 2

16 = $$d_2$$            Divide each side by 21

So, the length of the unknown diagonal of the rhombus is 16 inches.

Example 3: Calculate the area of a flower bed in the shape of a rhombus that has a side length of 9 feet and the perpendicular distance between the opposite sides being 7 feet.

Solution:

As stated in the question,

Side length of the flower bed, b = 9 feet

Height of the flower bed, h = 7 feet

A = b $$\times$$ h    Write the formula for the area of a rhombus

= 9 $$\times$$ 7    Substitute the values

= 63         Multiply

So, the area of the flower bed is 63 square feet.