Rhombus Formula

The rhombus formula is used to find the formulas associated with a rhombus. All four sides of a rhombus are equal thus it is also called an equilateral quadrilateral. The area of a rhombus is described as the two-dimensional space covered by the rhombus. Let us learn about the area of a rhombus formula with a few solved examples in the end.

What Is the Rhombus Formula?

The formulas for rhombus are defined for two features, an area of the rhombus and the perimeter of a rhombus. These rhombus formulas can be expressed as:

Rhombus formulas

Perimeter of a Rhombus Formula

The perimeter of a rhombus is the sum of its four sides, thus the perimeter of the rhombus formula = 4 × a, where 'a' is the side.

Area of a Rhombus Formula

To find the area of a rhombus, we find the total area enclosed by a rhombus. The area of the rhombus can be calculated by the following rhombus formulas:

When length of the diagonals are given, Area of a rhombus formula = 1/2 × \(d_1\) × \(d_2\)
When the length of the side of the rhombus and interior angle are given, Area of rhombus formula = a² × sin x

where,

\(d_1\) and \(d_2\)are the diagonals,
a is the length of the side of the rhombus,
x is the interior angle

Let us understand the rhombus formula better using a few solved examples.

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Examples on Rhombus Formulas

Example 1: Find the area of the rhombus of diagonal lengths 10 and 8 units using the rhombus formula.

Solution:

To find:
Area of the rhombus.
Using the rhombus formula,
Area of the rhombus = 1/2 × \(d_1\) × \(d_2\)
Area of the rhombus = 1/2 × 10 × 8
Area of the rhombus = 40

Answer: The area of the rhombus is 40 square units.

Example 2: Using the rhombus formula find the area of the rhombus with an interior angle of 30 degrees and length of the side 5in.

Solution:

To find: Area of the rhombus.

Interior angle(a) = 30 degrees, side length = 5 in.

Using the rhombus formula,

Area of the rhombus = a² × sin x

Area of the rhombus = 5² × sin 30

Area of the rhombus = 25 × 1/2

Area of the rhombus = 12.5

Answer: The area of the rhombus is 12.5 unit inches.

Example 3: A rhombus-shaped tile is placed at the playground of length 16 units. Can you find the perimeter of the tile using the rhombus formula?

Solution:

Given:
Length of the tile = 16 units.
Since all sides of a rhombus are equal, all four sides are equal to 16 units.
Perimeter = 4 × side = 4 × 16 = 64 units

Answer: The perimeter of the tile is 64 units.

FAQ's on Rhombus Formulas

What Are the Rhombus Formulas?

The formulae for rhombuses are defined for two parameters, area and perimeter:

Area of a rhombus = 1/2 × \(d_1\) × \(d_2\), where \(d_1\) and \(d_2\) are diagonals of a rhombus
The perimeter of a rhombus, where P = 4 × a, where 'a' is the side of the rhombus.

What Is the Perimeter of a Rhombus Formula?

The perimeter of a rhombus formula is defined as the sum of all four sides. It is expressed as the perimeter of a rhombus (P) = 4 × a, where 'a' is the side of the rhombus.

What Are the Area of a Rhombus Formulas?

Length of the diagonals = 1/2 × \(d_1\) × \(d_2\), where \(d_1\) and \(d_2\)are the diagonals.
Interior angles = a² × sin x. Where 'a' is the length of the side of the rhombus, and 'x' is the interior angle.

What Is the Rhombus Formula When the Two Diagonals are Given?

The area of a rhombus when diagonals are given is calculated by using the following rhombus formula.

The area of a rhombus formula = 1/2 × \(d_1\) × \(d_2\), where \(d_1\) and \(d_2\)are the diagonals.

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