Perimeter
What is perimeter?
- Perimeter is the total distance around the outside of a 2D shape
- It is found by adding the lengths of the sides together
- The perimeter of a circle is called the circumference
How do I find the perimeter of a 2D shape?
- To find the perimeter of any 2D polygon, add the lengths of its sides together
- For any regular 2D shape, the perimeter will be the number of sides, multiplied by the length of one side
- For example, the perimeter of a square of side length x cm will be 4x cm
- Often, the shape will not be a straight-forward 2D shape and you will need to use the information given to find the lengths of some of the sides
- Shapes made up of 2 or more 2D shapes are called compound shapes
- If the compound shape is made up of two rectangles, for example an L-shape, the length of two shorter sides opposite a longer side will add up to the same as the longer side
- If the compound shape is made up of other 2D shapes, you will need to use more information to find the lengths of the individual sides
- To do this you will need to be confident with the properties of 2D shapes
- Look out for sides that are equal, for example in a rectangle, parallelogram, or isosceles triangle.
- Dashes may be used to mark the equal sides, or the question may tell you which sides are equal
Examiner Tip
- Understanding how to find missing lengths of compound shapes can be essential for questions involving forming algebraic equations
- Try it with numbers and then see how that can be transferred to working with algebraic expressions
Worked example
The compound shape below consists of a rectangle with length 5 cm and width 4 cm and a second rectangle of length 15 cm and width 6 cm.
Find the perimeter of the compound shape.
The shape is made up of two rectangles, so all sides meet at right angles
The two shorter sides at the top will be equal to the 15 cm length at the bottom
The missing side on the left will be equal to the sum of the two shorter sides on the right
You can now find the sum of all the sides to find the total perimeter
P = 5 + 4 + 10 + 6 + 15 + 10 cm
You could also instead consider the four sides of the new, biggest rectangle
P = 2(10 + 15) cm
P = 50 cm