Perimeter in Maths

Perimeter is defined as the total length of all the sides of a closed figure. It is measured in units of length, such as meters, centimeters, or inches.

• The perimeter of a shape can be found by adding the lengths of all the sides. For example, a square with a side length of 5 m is 5 + 5 + 5 + 5, i.e., 20 m.
• The perimeter of a shape is the distance you cover when you walk around it.

Formulas for Perimeter

Different shapes have specific formulas to calculate their perimeter.

• Polygon: Sum of all sides
• Regular Polygon: Perimeter = n × side length

Common Shapes

How to Find Perimeter

To calculate the perimeter of any figure, we use the steps discussed below:

Step 1: Find the length of all the sides of the given figure and mark them as a, b, and c

Step 2: Find the sum of all the sides to get the perimeter of the figure.

Step 3: If the given figure is a curved figure we use other methods or formulas to find the perimeter of the figure.

Step 4: As the perimeter is nothing but the length of all the sides it is measured in units of length.

For example, suppose we have to find the perimeter of a square plot of side 10 m.

Side of Square (a) = 10 m

Perimeter of Square(P) = 4(a)

P = 4(10) = 40 m

Thus, the perimeter of the square feild is 40 m

Perimeter of Complex Shapes

The perimeter of complex shapes can be calculated by dividing them into simpler parts. Then, add the outer boundary lengths only.

For example, the perimeter of the following shape can be found by breaking it down into a rectangle and a triangle, as it is made of an isosceles triangle and a rectangle.

Solution:

• Sides of the Isosceles Triangle = 8 m
• Length of the Rectangle = 10 m
• Breadth of the Rectangle = 6 m

Observing the figure, the perimeter of the figure is,

Perimeter(P) = 8 + 8 + 10 + 10 + 6

P = 42 m

Also Check

• Area in maths
• Surface area and volume

Solved Examples

Example 1: Find the perimeter of a square with a side length of 5 meters.

Solution:

Given,

• Side of Square(a) = 5 m

Perimeter of Square(P) = 4a

P = 4(5)

P = 20 m

Thus, the perimeter of the square is 20 m.

Example 2: Find the perimeter of a rectangle with a length of 10 meters and a width of 5 meters.

Solution:

Given,

• Length of Rectangle(l) = 10 m
• Breadth of Rectangle(b) = 5 m

Perimeter of Rectangle(P) = 2(l+b)

P = 2(10+5)

P = 30 m

Thus, the perimeter of the rectangle is 30 m.

Example 3: Find the perimeter of a triangle with side lengths 3 meters, 4 meters, and 5 meters.

Solution:

Given,

• First Side (a) = 3 m
• Second Side (b) = 4 m
• Third Side (c) = 5 m

Perimeter of Triangle (P) = a + b + c

P = 3 + 4 + 5

P = 12 m

Thus, the perimeter of the triangle is 12 m

Example 4: Find the perimeter (circumference) of a circle with a radius of 7 meters.

Solution:

Given,

• Radius of Circle(r) = 7 m

Circumference of Circle(C) = 2πr

C = 2×22/7×7

C = 44 m

Thus, the circumference of the circle is 44 m.

Example 5: Find the perimeter of a trapezium with bases 6 meters and 8 meters and height 4 meters.

Solution:

Given,

• Base of Trapezoid, b₁ = 6 m and b₂ = 8 m
• Height of Trapezoid(h) = 4 m

Perimeter of Trapezium(P) = (b₁ + b₁) + 2h

P = (6+8) + 2(4)

P = 22 m

The Perimeter of the Trapezum is 22 m.