# Perimeter of Rhombus: Formula of Side and Diagonals, Examples

The Perimeter of a shape is the total distance around it. When it comes to a Rhombus all four sides are equal in length. Therefore, the Perimeter of a Rhombus can be acquired by adding all 4 sides or simply multiplying a side into four. Read on to learn more about the Perimeter of a Rhombus, the Formula to find the Perimeter of a Rhombus when the Sides and Diagonals are given in the question and Examples of the same.

## What is a Rhombus?

A Rhombus is a four-sided shape which is also called a quadrilateral where all four sides have the same length. Imagine the shape of a Diamond.

Furthermore, here are Points to Remember about a Rhombus:

• All sides of a Rhombus have equal lengths.
• Corresponding angles located on opposite sides are of equal measure.
• The opposite sides run parallel to each other.
• The total sum of any two neighbouring angles equals 180 degrees.
• Each diagonal divides the vertex angles into two equal parts.
• The diagonals intersect each other at right angles, hence dividing each other into equal parts.

## Perimeter of a Rhombus Formula when Sides are given

When the Sides of a Rhombus are given, the Formula is simple. As you are already aware the sides of a Rhombus are equal. Hence, to find out the Perimeter of a Rhombus you need to add up all the sides.

Perimeter = a + a + a + a

Or

Perimeter = 4 a (which means a is multiplied 4 times)

For Example, if the side given is 4 meters. Thus, the Perimeter shall be:

Perimeter = 4 + 4 + 4 + 4 = 16

Or

Perimeter = 4 ✕ 4 = 16

Therefore, the Perimeter of a Rhombus whose side is 4 meters is 16.

## Perimeter of a Rhombus Formula when Diagonals are given

A Rhombus has two diagonals that intersect with each other at Right angles = 90 degrees. Additionally, these Diagonals split the Rhombus into four right-angled triangles. The Diagonals of a Rhombus also bisect each other which means that they cut each other in half.

Things to keep in mind:

• When the Diagonals intersect, they create right-angled triangles inside the Rhombus.
• Moreover, each side of the Rhombus is the hypotenuse of these right-angled triangles.
• To find the side length of the Rhombus, you will need to use the Pythagorean theorem (a2 + b2 = c2) in one of these right-angled triangles.

To keep it simple, follow these steps along with the examples:

• Find the lengths of the diagonals.
• Suppose the lengths of the diagonals are 5 and 10.
• Square both lengths and add them together.
• 5= 25
• 102 = 100

25 + 100 = 125

• Take the Square root of that sum.
• Square Root of 125 = 11.18
• Multiply by 2 to get the Perimeter.
• 11.18 ✕ 2 = 22.36

Thus, the Perimeter of the Diagonals 5 and 10 is 22.36

## What is the Perimeter of Rhombus with Diagonals 10 and 24?

The Perimeter of Rhombus with Diagonals 10 and 24 is as follows:

10 = 102 = 100

24 = 242 = 576

100 + 576 = 676

The Square root of 676 = 26

26 ✕ 2 = 52

Thus, the Perimeter of Rhombus with Diagonals 10 and 24 is 52.

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