Perimeter — Mathematics, 11–13 years
Find the distance around a shape by adding its side lengths, and understand why different shapes can have the same perimeter.
What perimeter is
Perimeter is the total distance around the outside edge of a flat shape. Imagine walking exactly once along its boundary: the distance you walk is the perimeter. You find it by adding the lengths of all the sides, using the same unit throughout, such as centimetres or metres.
Why perimeter is useful
Many real problems ask how much material is needed around something, not across its whole surface. Fences, borders, frames and running tracks all have an outside distance to measure. Perimeter gives one reliable way to answer that question, even when the shape has several different sides.
Perimeter of an L-shape
An L-shaped garden has boundary sides of 8 m, 3 m, 4 m, 5 m, 4 m and 8 m. Add them in order around the edge: 8 + 3 + 4 + 5 + 4 + 8 = 32. The perimeter is 32 metres. Notice that we measure the outside boundary, not the two lengths that form the inside corner.
Perimeter is not area
A reasonable mistake is to multiply length by width whenever a rectangle appears. That calculation finds area, the amount of surface inside, because it counts rows of squares. Perimeter asks a different question: how far is it around the edge? For a rectangle, use 2 × length + 2 × width, and label the answer in length units.
Perimeter outside school
Perimeter helps when putting a border around a vegetable patch, buying skirting board, framing a picture or planning lights around a stage. You measure the boundary and choose enough material, usually with a little extra for joins or mistakes. It does not tell you how much paint or paving covers the inside; that is an area question.
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