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# 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:

### 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 = a
^{2}× 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.

## 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 = a^{2} × sin x

Area of the rhombus = 5^{2} × 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 = a
^{2}× 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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