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Perimeter is All Around

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The perimeter of a shape is the length of its boundary. We add the length of every side to find the perimeter.

Think of the small character walking all the way around the box shown below. The perimeter is what he walks around to get to back to where he started.

Hint: Perimeter and area are often taught at the same time and it can be easy to confuse one with the other. Think of a memory prompt to help remember which is which.

How about P for perimeter, P for post , Fence posts will go all the way around the perimeter.

4 by 3 box showing perimeter
First side 4 cm
Second side 3 cm
Third side 4 cm
Fourth side 3 cm
Total ( 4 + 3 + 4 + 3)= 14 cm

So what is the perimeter of the rectangle (the box) shown above?
It is 4 cm + 3 cm + 4 cm + 3 cm = 14 cm

Perimeter of a Rectangle

What do we know about a rectangle?

  • It has 4 sides
  • the opposite sides are equal so there are 2 sides of length and 2 sides of width
  • The perimeter = ( 2 x length) + (2 x width) which is ..
  • ..the same as 2 x (length + width)

Here are some examples

5  
  4

2 x Length = 2 x 5 = 10
2 x Width = 2 x 4 = 8
Perimeter = 10 + 8 = 18

or

Length + Width = 5 + 4 = 9
Perimeter = 2 x 9 = 18

 
4  
 
3

2 x Length = 2 x 4 = 8
2 x Width = 2 x 3 = 6
Perimeter = 8 + 6 = 14

or

Length + Width = 4 + 3 = 7
Perimeter = 2 x 7 = 14

 
  2  
   
6

2 x Length = 2 x 6 = 12
2 x Width = 2 x 2 = 4
Perimeter = 12 + 4 = 16

or

Length + Width = 6 + 2 = 8
Perimeter = 2 x 8 = 16

 
7  
  3

2 x Length = 2 x 7 = 14
2 x Width = 2 x 3 = 6
Perimeter = 14 + 6 = 20

or

Length + Width = 7 + 3 = 10
Perimeter = 2 x 19 = 20

A quick way to find the perimeter of a rectangles is to add the length and width and then multiply by 2

Perimeter of a Square

A square is a type of rectangle so we can use the same method for calculating perimeter although there is an even easier way: since the 4 sides of a square are the same length, we just need to add the length 4 times. e.g. for a square with a side of 5 we have a perimeter of 5 + 5 + 5 + 5. Or, even more quickly, we can take the length and multiply by 4.

5  
  5

Perimeter = 5 + 5 + 5 + 5 = 20

or

Perimeter = 4 x Length
Perimeter = 4 x 5 = 20

Perimeter of Polygons

You can find out more about different types of polygons here.

The perimeter of a polygon is the sum of the lengths of all its sides. The example below shows an irregular hexagon with a perimeter = 20 cm (3 cm + 3cm + 3cm +3cm + 4cm + 4cm)

irregular hexagon with perimeter of 20 cm

A polygon whose sides are equal is called a Regular Polygon. All angles of a Regular Polygon are also equal.

To find the perimeter of a regular polygon, multiply the length of the side by the number of sides.

 

Shape/ Description

Perimeter

 
Pentagon
5 equal-sided polygon
Perimeter = 5 x length of side
pentagon
Hexagon
6 equal-sided polygon
Perimeter = 6 x length of side
hexagon
Heptagon
7 equal-sided polygon
Perimeter = 7 x length of side
heptagon
Octagon
8 equal-sided polygon
Perimeter = 8 x length of side
octagon

Perimeter Worksheets

Use the printable worksheets listed below to practice calculating perimeters.

You will find other printable geometry worksheets here.

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