Perimeter
The perimeter is the total distance around the edge of a 2D shape. Since it is a length, the metric units for perimeter are millimetres (mm), centimetres (cm), metres (m) and kilometres (km).
Calculating Perimeters
The perimeter is found by adding together the lengths of each side.
Example
Image caption, Calculate the perimeter of this shape.
1 of 4
Question
Calculate the perimeter of this shape.
Perimeter = 6 + 3 + 1.5 + 2 + 7.5 + 5 = 25 m
A fence is built around the perimeter of a field. What is the total length of the fence?
Image caption, To calculate the perimeter, label the length of all the sides.
1 of 2
Question
Calculate the perimeter of an equilateral triangle with side length 5 cm.
Perimeter = 5 + 5 + 5 = 15 cm
Calculating perimeters of shapes with missing lengths
Sometimes there are lengths of sides missing. To calculate the perimeter:
- Find the lengths of the missing sides and mark them on the shape.
- Calculate the perimeter by adding all of the sides together.
Example
Calculate the perimeter of this shape.
Find the lengths of the missing sides and mark them on the shape.
Calculate the perimeter by adding all of the sides together.
Perimeter = 3 + 5 + 8 + 5 + 3 + 8 + 14 + 8 = 54 cm
Question
Calculate the perimeter of the sign which is made from an equilateral triangle with side length 20 cm and a rectangle of length 60 cm.
Since the triangle is equilateral, all sides are 20 cm.
The side highlighted in red is part of the triangle and the rectangle, so the height of the rectangle is 20 cm.
The side highlighted in red is not part of the perimeter of the whole shape.
Calculating missing lengths given the perimeter
In some questions the perimeter will be given and one or more sides could be unknown.
Example
Calculate the width of a rectangle with perimeter 54 cm and height 12 cm.
Perimeter = 2 x height + 2 x width
54 = 2 x 12 + 2 x width
54 = 24 + 2 x width
54 鈥 24 = 2 x width
30 = 2 x width
Width = 30 梅 2 = 15 cm
Test yourself
More on M1: Geometry and measures
Find out more by working through a topic
