Perimeter Of A Rhombus- Definition, Formula, Examples

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.

Free Demo Classes

Register here for Free Demo Classes

Select Course CUET Digital Marketing NDA Graphics Designing MS Excel (10 Hrs.) Interview Skill Course Entrepreneurship Programme Content Writing

Related Links-

• Volume Of A Sphere
• CM To Inches (cm to in) Converter
• Roman Numeral Conversion 

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
   

5. 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

6. 6. So, the perimeter of the rhombus will be equal to 2 × 

   (a2+b2)−−−−−−−√(a2+b2)
   .

You may also read-

• Perimeter of a rectangle
• Area of a square
• Area of a rectangle

 

 

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