Area and perimeter
Perimeter
Perimeter is the distance all the way round the edge. Walk round the shape and add up every side you travel along.
What perimeter means
The PERIMETER of a shape is the total distance around its edge. To find it, add up the lengths of ALL the sides. Because it is a length, perimeter is measured in units like cm, m or km — never in square units.
Rectangles
A rectangle has two pairs of equal sides, so there are two easy ways: Add all four: 5 + 3 + 5 + 3 = 16 cm Or double the sum: (5 + 3) × 2 = 16 cm Both give the same answer. The second is quicker once you trust it.
Shapes with more sides
For an L-shape or any other polygon, the method is the same — just be systematic. Start at one corner and work all the way round in one direction, adding as you go, until you are back where you started. Mark each side as you use it. The commonest mistake is missing a side or counting one twice.
Same perimeter, different area
Two shapes can have exactly the same perimeter but enclose different amounts of space. A 1 × 7 rectangle has perimeter 16 cm and area 7 cm². A 4 × 4 square also has perimeter 16 cm but area 16 cm². So perimeter does not decide area. For a fixed perimeter, the closer a shape is to a square, the more area it encloses.
Worked examples
Perimeter of a rectangle
- The sides are 5 cm and 3 cm.
- Add all four: 5 + 3 + 5 + 3.
Answer: The perimeter is 16 cm
Using the doubling shortcut
- Add one long and one short side: 5 + 3 = 8.
- Double it, because there are two of each.
Answer: 16 cm
Perimeter of an L-shape
- Start at one corner and go round in one direction.
- Add each side in turn: 2 + 4 + 3 + 2 + 5 + 2.
- Check you finish where you started.
Answer: The perimeter is 18 cm
Perimeter of a square
- All four sides of a square are equal.
- If one side is 6 cm, multiply by 4.
Answer: The perimeter is 24 cm
Same perimeter, different area
- A 1 × 7 rectangle: perimeter 16 cm, area 7 cm².
- A 4 × 4 square: perimeter 16 cm, area 16 cm².
Answer: Same perimeter, very different areas
Where you see this in real life
- Working out how much fencing you need to go round a garden.
- Measuring the ribbon needed to edge a picture frame.
- Finding the distance round a running track.
Key words
- Perimeter
- The total distance around the edge of a shape.
- Polygon
- A shape with straight sides.
- Side
- One of the straight edges of a shape.
- Rectangle
- A four-sided shape with four right angles.
- Estimate
- A rough answer worked out before measuring.
- Centimetre (cm)
- A unit of length.