Area measures the space inside a shape. Perimeter measures the distance all the way around it, like a fence around a garden. You already measure lengths; perimeter adds them up.
Why it works
Walk around the edge of a shape and add up the length of each side you walk along. That total is the perimeter. It is a length, so it is measured in units like centimeters, not square units. Area and perimeter measure different things, so the same rectangle can have an area of 15 square units and a perimeter of 16 units.
Key idea
Perimeter = the sum of all the side lengths. In a rectangle, opposite sides are equal, so add length + width + length + width.
Worked example: A rectangle
A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
- Sides: 5, 3, 5 and 3 cm.
- $5 + 3 + 5 + 3 = 16$.
Answer: 16 cm
Worked example: A triangle
A triangle has sides of 4 in, 6 in and 7 in. What is its perimeter?
- $4 + 6 + 7 = 17$.
Answer: 17 inches
Worked example: On a grid
A shape on a grid of 1-centimeter squares has sides of 4, 2, 2, 1, 2 and 3 cm, going around. What is its perimeter?
- Add every side once: $4 + 2 + 2 + 1 + 2 + 3 = 14$.
Answer: 14 cm
Common mistake
Mixing up area and perimeter. Area counts squares inside; perimeter adds lengths around. Ask: am I covering it or going around it?
Counting corner squares twice. On a grid, count the unit edges along the outside, not the squares next to the edge. A corner square touches the edge on two sides, so counting squares gives the wrong total.
Counting corner squares twice. On a grid, count the unit edges along the outside, not the squares next to the edge. A corner square touches the edge on two sides, so counting squares gives the wrong total.