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. 
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 the crochet or ribbon required to cover the border of a table mat. 

Perimeter of things around us in the real world

 

How to find perimeter?

We use a ruler to measure 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 string of thread and place it exactly along the boundary of the shape, once. The total length of the string used 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 Polygons Irregular Polygons
4cm square irregular shape

Perimeter = 4 + 4 + 4 + 4

               = 16 cm

               OR

Perimeter 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 perimeter of some common shapes is calculated: 

Polygon name : Polygon Picture/Image : Perimeter Formula :
Equilateral Triangle

triangle

P = 3 x a
Scalene Triangle scalene triangle P = a + b + c
Square square P = 4 x a
Rectangle rectangle P = 2 ( a + b )
Quadrilateral quadrilateral P = a + b + c + d
Regular Pentagon regular pentagon P = 5 x a
Regular Hexagon regular hexagon P = 6 x a 
Regular Octagon 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 lenght of the sides.

 

  Fun Facts

  • The Perimeter of a circle is called the circumference. Circumference is calculated using the formula 2π × r .
 

let's sing Let's sing!

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

related math vocabularyRelated math vocabulary

Length, Ruler, Polygon
 

Frequently Asked Questions

  • How can we find the perimeter of regular shapes?

    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.

  • How can we find the perimeter of irregular shapes?

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

  • What are some uses of the perimeter in day-to-day life?

    Some real-life examples where perimeter is used are: - Fencing off a crop field. - Building a barn for horses. - Planning the construction of a house/swimming pool.

  • Is the circumference of a circle the same as its perimeter?

    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.

Practice Problems on Perimeter

Pick the correct answer
1.   What is the perimeter of a square of side 5 units?
2.   The perimeter of an equilateral triangle is 18 cm. What is the side length of the triangle?
3.   The perimeter of a regular polygon is 21 units. If each side of the polygon is 3 units, how many sides does the polygon have?
4.   How does the perimeter of a square change if its sides are increased by 2 cm?
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