Perimeter: the distance around
The perimeter of a closed shape is the total length of its boundary. Imagine walking once around the edge of a field: the distance you walk is the perimeter.
For any polygon, add the lengths of all its sides.
Example. A triangle has sides 5 cm, 7 cm and 8 cm. Its perimeter is 5 + 7 + 8 = 20 cm.
Perimeter of a rectangle
A rectangle has two lengths (l) and two breadths (b):
Perimeter of a rectangle = 2 × (l + b)
Perimeter of a square
All four sides of a square are equal:
Perimeter of a square = 4 × side
For any regular polygon (all sides equal), the perimeter is the number of sides × the length of one side. A regular hexagon with side 6 cm has perimeter 6 × 6 = 36 cm.
Perimeter is a length, so it is measured in mm, cm, m or km.
Area: the space inside
The area of a shape is the amount of surface it covers. We measure it by counting how many unit squares fit inside it.
A square with sides of 1 cm has an area of 1 square centimetre (1 cm²).
Larger areas are measured in square metres (m²) or square kilometres (km²).
Area of a rectangle
A rectangle 4 cm long and 3 cm wide can be covered by 3 rows of 4 unit squares, which is 12 squares. So:
Area of a rectangle = length × breadth
Area of a square
Area of a square = side × side
Example. A square tile has a side of 20 cm. Its area is 20 × 20 = 400 cm².
Area of irregular shapes
For a shape drawn on squared paper, count:
each full square as 1,
each square that is more than half covered as 1,
each square that is exactly half covered as ½,
and ignore squares that are less than half covered.
This gives a good estimate of the area.
Same perimeter, different area
Shapes with the same perimeter can have very different areas.
Rectangle | Perimeter | Area |
|---|---|---|
9 cm × 1 cm | 20 cm | 9 cm² |
7 cm × 3 cm | 20 cm | 21 cm² |
5 cm × 5 cm | 20 cm | 25 cm² |
For a fixed perimeter, the square encloses the largest area of all the rectangles.
Word problems
Example 1. A rectangular park is 80 m long and 50 m wide. How much fencing is needed to go around it once?
Fencing goes around the boundary, so we need the perimeter: 2 × (80 + 50) = 260 m.
Example 2. How many square tiles of side 25 cm are needed to cover a floor 5 m long and 4 m wide?
First use the same units: 5 m = 500 cm and 4 m = 400 cm.
Area of floor = 500 × 400 = 200 000 cm²
Area of one tile = 25 × 25 = 625 cm²
Number of tiles = 200 000 ÷ 625 = 320 tiles
Example 3. The area of a rectangle is 48 m² and its length is 8 m. Find its breadth.
Breadth = area ÷ length = 48 ÷ 8 = 6 m.
Tips
Ask yourself: is the question about the boundary (perimeter) or the surface (area)?
Convert all measurements to the same unit before calculating.
Write units with your answer: cm for perimeter, cm² for area.