How to find the Perimeter of A Rhombus?
A rhombus is a parallelogram such that its four sides are equal to each other. It can be interpreted as an equilateral quadrilateral. The opposite sides of a rhombus are parallel to each other and its opposite angles are equal. The diagonals of a rhombus meet each other at 90o and equally divide the vertex angles. A square can also be termed a rhombus as it satisfies all its properties.
The above figure depicts a rhombus ABCD with sides AB, BC, CD and AD of equal length and diagonals AC and BD dividing each other into two equal parts.
Perimeter of a Rhombus Formula
The perimeter of a rhombus is equal to the sum of all its side lengths. Since all sides of a rhombus are equal to each other, its perimeter is defined as four times one of its side lengths. For example, if one side of a rhombus measures x units, its perimeter is given by 4x units.
P = 4a
where,
P is the perimeter of rhombus,
a is the side of rhombus.
Sample Problems
Problem 1. Find the perimeter of a rhombus if its side length is 4 m.
Solution:
We have, a = 4.
Using the formula we get,
P = 4a
= 4 (4)
= 16 m
Problem 2. Find the perimeter of a rhombus if its side length is 7 m.
Solution:
We have, a = 7.
Using the formula we get,
P = 4a
= 4 (7)
= 28 m
Problem 3. Find the perimeter of a rhombus if its side length is 10 m.
Solution:
We have, a = 10.
Using the formula we get,
P = 4a
= 4 (10)
= 40 m
Problem 4. Find the perimeter of a rhombus if its side length is 12 m.
Solution:
We have, a = 12.
Using the formula we get,
P = 4a
= 4 (12)
= 48 m
Problem 5. Find the side length of a rhombus if its perimeter is 96 m.
Solution:
We have, P = 96
Using the formula we get,
P = 4a
=> a = P/4
=> a = 96/4
=> a = 24 m
Problem 6. Find the side length of a rhombus if its perimeter is 52 m.
Solution:
We have, P = 52
Using the formula we get,
P = 4a
=> a = P/4
=> a = 52/4
=> a = 13 m
Problem 7. Find the side length of a rhombus if its perimeter is 100 m.
Solution:
We have, P = 100
Using the formula we get,
P = 4a
=> a = P/4
=> a = 100/4
=> a = 25 m
