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.

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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

 

 

Solved examples

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

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