# Perimeter Of A Rhombus- Definition, Formula, Examples

Safalta expert Published by: Yashaswi More Updated Sat, 09 Sep 2023 12:17 PM IST

## Highlights

Check out how to find the Perimeter Of Rhombus - Definition, Formula, Examples here at Safalta.com

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A rhombus is a flat form with four angles that aren't always 90 degrees and four equal sides. Often referred to as a diamond or diamond-shaped object, a rhombus. The perimeter of a rhombus is the entire distance traversed along its edge. Because a square meets all the criteria for becoming a rhombus, we can also refer to it as one. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty. Our online school aims to help students prepare for Board Exams by ensuring that study they have conceptual clarity in all the subjects and can their maximum in the exams.

Source: Safalta.com

You may also read Area Of A Rhombus

Rhombus has:

• All sides of equal length.
• Opposite sides have to be parallel.
• The altitude is a distance at right angles between two parallel sides.
• The diagonals of a rhombus bisect each other at 90 degrees.

## The formula of the Perimeter of the Rhombus

The perimeter of a rhombus is given as:

### P=4×a

Here, a = Length of the side of the rhombus

## The perimeter of the Rhombus Formula With Diagonals

The Pythagoras theorem is used to calculate the side length of a rhombus when the length of its diagonals is known. In this case, we employ the rhombus's following properties:
• The two diagonals of a rhombus split it into four congruent right-angled triangles.
• The diagonals intersect at right angles.
1. Consider a rhombus PQRS with diagonals a and b, and center O.

2. Pick a triangle, say POS. Since the diagonals of a rhombus bisect each other at right angles, the length of OP will be

a2a2
and OS will be
b2b2
3. Assume that the side of the rhombus is X.

4. Using Pythagoras theorem in triangle POS, we get:

X2 = a22+b22a22+b22

, which gives us,

X2 =

(a2+b2)4(a2+b2)4

X =

(a2+b2)2−−−−−−−−√(a2+b2)2

1. Substitute the value of X in the perimeter of the rhombus formula i.e. 4X. You will get:

4 ×

(a2+b2)2−−−−−−−−√(a2+b2)2
1. 6. So, the perimeter of the rhombus will be equal to 2 ×

(a2+b2)−−−−−−−√(a2+b2)
.

### Question: Find the perimeter of a rhombus having a side of 5 cm.

Solution:

Given,
a = 5 cm

The perimeter of a rhombus = 4 × a
The perimeter of a rhombus = 4 × 5
The perimeter of a rhombus = 20 cm

## How do you find the perimeter of a rhombus?

The perimeter of a rhombus is the sum of all its sides. Since all the four sides of a rhombus are equal, the formula used to find the perimeter of a rhombus is: Perimeter = a + a + a + a = 4a, where 'a' represents the side length of the rhombus.

## What is the formula of area and perimeter of rhombus?

Area l × b ½ × d1 × d2
Perimeter 2 × (l + b) 4a

## What is a formula of rhombus?

Area of Rhombus Formula.
Formulas to Calculate Area of Rhombus
Using Base and Height A = b × h
Using Trigonometry A = b2 × Sin(a)

## Is the perimeter of a rhombus whose diagonals are 16 and 30?

The perimeter of a rhombus whose diagonals are 16 cm and 30 cm is 68 cm.

## Are all sides of rhombus equal?

All sides of a rhombus are equal. Here, AB = BC = CD = DA. Opposite sides are parallel in a rhombus. Opposite angles are equal in a rhombus.

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