# What is the perimeter?

## What is the perimeter?

**The perimeter is the distance around the edge of a 2D shape. **At primary school, teachers will sometimes talk about an ant walking around the edge of a shape to make this concept clear to the children.

## Calculating the perimeter

Children start to learn about perimeter in **Year 4**. They may be asked to measure the length of each side of the shape and then add these measurements up to find the perimeter. Alternatively, they may be given a shape like the following, which is not drawn to scale, and asked to find the perimeter:

At this point, they would need to understand that a rectangle has two long sides that are exactly the same length and two short sides that are exactly the same length, which is why only two measurements are given above. They could then work out the perimeter in any of the following ways:

10 + 4 + 10 + 4 OR (10 x 2) + (4 x 2) OR (10 + 4) x 2

**The perimeter of a shape is always calculated by adding up the length of each of the sides.**

In **Year 5 and 6**, children might be given shapes like this one and asked to find their perimeter:

In this case, they need to work out the lengths of the edges that are unlabelled, by looking at the other labelled edges.

In this case, you can work out that the unlabelled small side on the shape is 2cm long, since it must be the length of the bottom edge (9cm) minus the two top edges (4cm and 3cm).

To find out the perimeter, you would then need to add up all the sides: 4 + 5 + 9 + 6 + 3 + 3 + 2 + 2 = 34cm.

## Perimeter puzzles in KS2

Often, children will be given worded puzzles or investigations in which they will have to visualise a shape in order to find the answer, for example:

*A rectangle has an area of 20cm². What could its perimeter be?*

- In this case, the child would need to work out what length the sides could be in order to have an area of 20cm².
- They would need to remember that the formula for area is length x width, so they may come to the conclusion that the sides of the rectangle are 4cm and 5cm.
- They would then need to work out the perimeter (4 + 4 + 5 + 5 ) and would come to the answer 18cm.

It is essential that children become familiar with problems like this, where they are required to visualise shapes that have not been drawn. It can be helpful for children to draw rough, unmeasured shapes to help them solve these problems.

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