Perimeter on a grid

The perimeter is the distance around the outside of a closed 2D shape, space or area.

You see the perimeter in real life on a football pitch or around a house to show its boundary.

You can only find the perimeter if the shape, area or space is closed. You cannot find the perimeter of a shape if a side is open.

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The perimeter can be measured in millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

The unit of measure you use depends on the size of the perimeter that you want to work out.

If you are measuring the perimeter of this hexagon, you would use cm. You would not use metres because the shape is small, so it needs a smaller measure.

If you were measuring the perimeter of a football pitch, because it is much larger, you would use metres.

Calculating the perimeter on a grid

To calculate the perimeter, we find the total length of all the sides.

This rectangle has been drawn on centimetre squared paper, so you can count the squares to work out the lengths and widths and record the answer in centimetres.

Have you noticed the pink dot?

This is to mark the starting point. You don’t want to miss any squares out or count some more than once!

Start at the dot and move clockwise around the outside of the shape, counting the squares and labelling the sides, until you get back to the pink dot.

Next, you need to work out the total, so you add the measurements up.

5cm + 4cm + 5cm + 4cm = 18cm

The perimeter equals 18cm. You can write it like this:

P = 18cm

Calculating the perimeter of rectilinear shapes

Not all perimeters look like rectangles or shapes you recognise. However, you can find the perimeter of shapes like this in exactly the same way.

First, you place the dot, so you know where to start and finish.

Then, you count the squares along all the sides of the shape and label them.

Next, you calculate the perimeter by finding the total of all the sides.

P= 5cm + 7cm + 8cm+ 2cm + 3cm + 5cm

Before you start calculating from left to right, look to see if there are any numbers you find easy to calculate mentally.

You can see different pairs to 10, so you can use them to help calculate the perimeter.

5cm + 5cm = 10cm

7cm + 3cm = 10cm

8cm + 2cm = 10cm

You know that three lots of 10cm equals 30cm.

P = 30cm

Here is a rectangle on a 1cm squared grid.

Example 2

Here is a rectilinear shape drawn on a 1cm squared grid.