Perimeter – Definition with Examples

What Is Perimeter? 

In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.

The word perimeter has been derived from the Greek word ‘peri’ meaning around, and ‘metron’, which means measure. The perimeter is the total length of the sides of a two-dimensional shape. 

We often find the perimeter when putting up Christmas lights around the house or fencing the backyard garden. Other examples may include finding the total length of the boundary of the soccer field or the length of ribbon required to cover the border of a place mat. 

How to Find a Perimeter?

We use a ruler to measure the length of the sides of a small regular shape. The perimeter is determined by adding the lengths of the sides/edges of the shape. 

For small irregular shapes, we can use a length of string or thread and place it exactly along the boundary of the shape. The total length of the string used once along the boundary is the perimeter of the shape.

The perimeter of all polygons can be determined by adding the lengths of their sides/edges.

Regular Polygons	Irregular Polygons
Perimeter = 4 + 4 + 4 + 4               = 16 cm               ORPerimeter of regular polygons = number of sides x length of one side = 4 x 4 = 16	Perimeter of irregular polygons = 5 + 3 + 2 + 4 + 3 + 7 = 24 cm

Here’s how the perimeters of some common shapes are calculated: 

Polygon name	Polygon Picture/Image	Perimeter Formula
Equilateral Triangle		P = 3 x a
Scalene Triangle		P = a + b + c
Square		P = 4 x a
Rectangle		P = 2 ( a + b )
Quadrilateral		P = a + b + c + d
Regular Pentagon		P = 5 x a
Regular Hexagon		P = 6 x a
Regular Octagon		P = 8 x a
Regular N-gon	A regular n-gon with each side a units long	P = n x a, where n is the number of sides and a is the length of the sides.

Fun Fact The perimeter of a circle is called the circumference. Circumference is calculated using the formula 2π × r .

 Let’s sing!

To put up a fence around a movie theatre,
First, Peter found its perimeter.
He added the lengths of all the sides, 
and fenced it with flowers big and wide.

 Let’s do it!

Instead of giving your children math practice worksheets on perimeter, give them craft material, like craft paper, crayons, and glue, and ask them to create a rectangular greeting card with a border on all its sides. You can also show them objects and ask them what the perimeter is. You can discuss how the perimeter of each of those objects can be calculated.  

Related Math Vocabulary

Length, Ruler, Polygon

Practice Problems

Perimeter Attend this Quiz & Test your knowledge. 1The perimeter of a regular polygon is 21 units. If each side of the polygon is 3 units, how many sides does the polygon have? 7 18 24 63 CorrectIncorrect Correct answer is: 7 The perimeter of a regular polygon is number of sides ✕ length of each side, which is equal to 21 units. So, the number of sides of the polygon should be perimeter/length of each side, i.e., 21 units/3 units or 7. 2The perimeter of an equilateral triangle is 18 cm. What is the side length of the triangle? 6 cm 9 cm 36 cm 54 cm CorrectIncorrect Correct answer is: 6 cm The perimeter of an equilateral triangle is 3 ✕ side which, is equal to 18 cm. So, the side of the equilateral triangle should be perimeter/3, i.e., 18 cm/3 or 6 cm. 3How does the perimeter of a square change if its sides are increased by 2 cm? Decreases by 2 cm Increases by 2 cm Increases by 4 cm Increases by 8 cm CorrectIncorrect Correct answer is: Increases by 8 cm The perimeter of a square is 4 ✕ side. So, if each side of the square increases by 2 cm, the perimeter will also increase by 4 ✕ 2 cm or 8 cm. 4What is the perimeter of a square of side 5 units? 10 units 15 units 20 units 25 units CorrectIncorrect Correct answer is: 20 units The perimeter of a square is 4 ✕ side, i.e., 4 ✕ 5 units or 20 units.

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