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Perimeter — Mathematics, 7–10 years

Find the distance all the way around a shape by adding its side lengths, and keep it distinct from the space inside.

The distance around

Perimeter is the total length of a shape’s boundary: the path you would walk around its edge. Add every side once. A rectangle that is 8 cm long and 5 cm wide has four boundary sides, so its perimeter is measured in centimetres, not square centimetres.

Why measure the edge?

Sometimes the question is not how much space a shape covers, but how much material is needed to go around it. People measure perimeters to make fences, borders and frames. Adding the sides solves that problem because a complete trip around the boundary is made from those side lengths.

An 8 cm by 5 cm rectangle

Start at one corner and add the four sides: 8 + 5 + 8 + 5. First, 8 + 5 = 13; then 13 + 8 = 21; finally 21 + 5 = 26. The perimeter is 26 cm. The two 8 cm sides match, as do the two 5 cm sides, so 2 × 8 + 2 × 5 also gives 26 cm.

Around is not inside

A common mistake is to count the squares inside a shape or multiply length by width when the question asks for perimeter. This is reasonable because both measurements use the same drawing and both can involve length and width. Check the wording: a fence follows the edge; tiles cover the inside.

Where it helps

Perimeter is useful when ribbon must go around a present, paint needs a border, or a garden needs a fence. If a rectangular garden measures 6 m by 4 m, 6 + 4 + 6 + 4 = 20 m of fencing is needed, before allowing for a gate or overlap.

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