Perimeter of polygons

Walking around a shape

The perimeter of a shape is the distance all the way around its edge. If you walked around a garden and measured every step along the fence, the total would be the perimeter. Perimeter is measured in ordinary length units: millimetres, centimetres, metres or kilometres.

To find a perimeter, add the length of every side. The rectangle below is 8 m long and 5 m wide. A walk around it goes 8 + 5 + 8 + 5 = 26, so the perimeter is 26 m. The two long sides and the two short sides each appear twice in the sum.

Squares and rectangles

A rectangle has a shortcut, because its sides come in two equal pairs. Add the length and the width once, then double: perimeter = 2 × (length + width). For the rectangle above, 2 × (8 + 5) = 2 × 13 = 26 m. The answer is the same, with less adding.

A square is a rectangle with four equal sides, so the shortcut is even shorter: perimeter = 4 × side. A square with a side of 7 cm has a perimeter of 4 × 7 = 28 cm. A square is the only rectangle where one side is enough to know all four.

Polygons with more sides

A polygon is any closed shape with straight sides, such as a triangle, a pentagon or a hexagon. It has no shortcut like a square, so the rule is always the same: add every side, one at a time. Walk around the shape in your head and say each number as you pass it.

Finding a missing side

Sometimes the perimeter is known and one side is missing. Work backwards. Take the sides you know away from the perimeter, and the number that is left is the missing side. A triangle with a perimeter of 18 cm and two sides of 5 cm and 6 cm has a third side of 18 - 5 - 6 = 7 cm.

For a rectangle with a known perimeter and length, do the same in two steps. Take away both lengths, then share the rest between the two equal widths. The worked example below uses that method from start to finish.