Perimeter – Definition with Examples

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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.

Perimeter of shape boundary

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. 

Perimeter of things around us in the real world

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.

How to find the perimeter with ruler and thread string

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

Regular PolygonsIrregular Polygons
4cm squareirregular shape
Perimeter = 4 + 4 + 4 + 4               = 16 cm               ORPerimeter of regular polygons = number of sides x length of one side = 4 x 4 = 16Perimeter 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 TriangletriangleP = 3 x a
Scalene Trianglescalene triangleP = a + b + c
SquaresquareP = 4 x a
RectanglerectangleP = 2 ( a + b )
QuadrilateralquadrilateralP = a + b + c + d
Regular Pentagonregular pentagonP = 5 x a
Regular Hexagonregular hexagonP = 6 x a 
Regular Octagonregular octagonP = 8 x a
Regular N-gonA regular n-gon with each side a units longP = 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 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 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.  

LengthRulerPolygon

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.

Frequently Asked Questions

All sides of a regular shape are equal. To find the perimeter of a regular shape, multiply the number of sides by the length of each side.

An irregular shape has sides with different lengths. So, to find the perimeter of an irregular shape, add the length of all the sides.

Some real-life examples where perimeter is used are: fencing of a crop field, building a barn for horses, planning the construction of a house/swimming pool.

Yes, the circumference of a circle is the same as its perimeter. It is the length of the circle’s boundary. The formula to calculate the circumference of a circle with radius r is 2𝜋r.


Perimeter – Definition with Examples

Shapes

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Perimeter – Definition with Examples

Angles

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Perimeter – Definition with Examples

Parallel and Perpendicular Lines

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