Area and perimeter
Area
Area is the amount of space inside a shape. It is measured in squares — which is why the units have a little 2.
Counting squares
The AREA of a shape is the space inside it, measured in SQUARE units. On squared paper, count the squares the shape covers. A shape covering 12 squares of 1 cm each has an area of 12 cm². The small 2 in cm² means 'square centimetres'. Using cm instead of cm² is a mistake worth avoiding — it changes the meaning entirely.
The rectangle rule
Counting every square is slow. For a rectangle there is a shortcut: Area = length × width A rectangle 5 cm by 3 cm has area 5 × 3 = 15 cm². It works because the rectangle is 3 rows of 5 squares — and that is exactly what multiplication counts.
Part squares
For a shape that does not fit the grid neatly, estimate. Count all the whole squares. Then count the part squares and pair them up — two halves make one whole. A part bigger than half counts as one; a part smaller than half counts as none. This gives a good estimate, not an exact answer, and that is fine.
Area and perimeter are different
PERIMETER is the distance round the edge, measured in cm. AREA is the space inside, measured in cm². The units are your clue: if the answer has a little 2, it is an area. And remember two shapes can share a perimeter but have different areas — a 1 × 7 rectangle and a 4 × 4 square both have perimeter 16 cm, but areas of 7 cm² and 16 cm².
Worked examples
Area by counting squares
- The shape covers 12 whole squares on 1 cm paper.
- Each square is 1 cm².
Answer: The area is 12 cm²
Area of a rectangle
- The rectangle is 5 cm long and 3 cm wide.
- Area = length × width = 5 × 3.
Answer: The area is 15 cm²
Area of a square
- A square with sides of 4 cm.
- Area = 4 × 4.
Answer: The area is 16 cm²
Estimating with part squares
- Count the whole squares: 9.
- Pair up the part squares — four halves make 2 more.
Answer: About 11 cm²
Which is area and which is perimeter?
- One answer is 16 cm, the other 16 cm².
- The little 2 means square units.
Answer: 16 cm² is the area; 16 cm is the perimeter
Where you see this in real life
- Working out how much carpet is needed to cover a floor.
- Finding how much paint you need for a wall.
- Comparing two gardens to see which has more growing space.
Key words
- Area
- The amount of space inside a shape.
- Square centimetre (cm²)
- A square 1 cm by 1 cm, used to measure area.
- Length
- How long a shape is.
- Width
- How wide a shape is.
- Perimeter
- The distance around the edge of a shape.
- Estimate
- A close answer rather than an exact one.