Perimeter: The Way Round

Ana has a small vegetable garden behind her house in Lisbon. It is a rectangle, 6 metres long and 4 metres wide. Rabbits keep eating her lettuces, so she wants to put a low fence all the way round it. How many metres of fence should she buy?

Walking round the edge

Imagine walking along the edge of the garden, starting at one corner and going round until you are back where you started. You walk along each side once:

6 m along the first long side,
4 m along the short side,
6 m along the other long side,
4 m back along the last short side.

6 + 4 + 6 + 4 = 20, so Ana needs 20 metres of fence.

A rectangular garden 6 m long and 4 m wide, seen from above, with a dotted amber path running all the way round its edge and an arrow showing the way round. The four sides are labelled 6 m, 4 m, 6 m and 4 m

The whole distance round the edge of a shape is called its perimeter. The word comes from Greek: peri means "around" and metron means "measure". A perimeter is a length, so it is measured in the units of length: centimetres, metres, kilometres.

Any shape with straight sides

The same idea works for every polygon: add up the lengths of all its sides. For a triangle with sides 3 cm, 4 cm and 5 cm:

3 + 4 + 5 = 12, so the perimeter is 12 cm.

For an odd shape, like an L, count the sides carefully. It is easy to miss a short one. A good habit is to put your finger on one corner and go round, saying each length out loud, until your finger is back at the start.

Two shapes with their sides labelled: a triangle with sides 3 cm, 4 cm and 5 cm, and an L-shaped figure with six sides of 6 cm, 2 cm, 4 cm, 3 cm, 2 cm and 5 cm. A small dot marks where to start going round each one

The L-shape has six sides: 6 + 2 + 4 + 3 + 2 + 5 = 22, so its perimeter is 22 cm.

A short cut for rectangles

A rectangle has two long sides of the same length and two short sides of the same length. So you can add one long side and one short side, and then double the answer. For Ana's garden: 6 + 4 = 10, and 10 × 2 = 20 metres, the same as before.

In words: the perimeter of a rectangle is twice the length plus the width. A square has four equal sides, so its perimeter is 4 × one side: a square tile with sides of 30 cm has a perimeter of 4 × 30 = 120 cm.

Try it at home

Use a tape measure or a ruler to measure the sides of a book. Add them up to find its perimeter.
Take a piece of string and lay it all the way round the edge of a plate or a box lid. Straighten the string and measure it. That is the perimeter too.
A square photo frame has sides of 15 cm. What is its perimeter?

Answers: 3. 4 × 15 = 60 cm.

Words to know

perimeter - the whole distance round the edge of a shape; for a polygon, the lengths of all its sides added up

Big idea

The perimeter is the length of the way round a shape. Add up every side; for a rectangle, add the length and the width and double it.