The idea, step by step
Cover a surface with square units
Area measures how much surface a shape covers. Imagine covering a rectangle with unit squares, without gaps or overlaps. Each square has a side length of one unit and an area of one square unit.
If each row contains 4 unit squares and there are 3 rows, there are 3 groups of 4 squares. Counting by multiplication gives 4×3=12 square units.
Use length times width
The rectangle formula is area=length×width. The side lengths must use the same unit before you multiply. The answer uses square units: centimetres multiplied by centimetres gives square centimetres.
Perimeter measures the boundary and area measures the inside. They answer different questions. A shape can have the same area as another rectangle but a different perimeter.
A common trap
To find rectangle area, add all four side lengths.
Instead: Adding the boundary lengths finds perimeter. Area counts the square units inside, using length×width.
See the thinking
Worked example 1
Find the area of a rectangle 8 centimetres long and 5 centimetres wide.
- One row contains 8 one-centimetre squares. There are 5 such rows.
- 8×5=40 square centimetres.
Worked example 2
A rectangle is 2 metres long and 50 centimetres wide. Find its area in square centimetres.
- Convert the length to 200 centimetres so both side units match.
- 200×50=10,000.
Check your understanding
A rectangle has 6 rows of 9 unit squares. What is its area?
Show answer
54 square units.
6×9=54.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Find the area of a 7 cm by 4 cm rectangle.1 mark
- Find the area of a 12 m by 3 m rectangle.1 mark
- Find the area of a square with side 9 cm.1 mark
- A grid has 5 rows and 8 columns of one-centimetre squares. Find its area.1 mark
- A rectangle is 1 m long and 30 cm wide. Find its area in square centimetres.2 marks
- A 6 cm by 4 cm rectangle has perimeter 20 cm. Is its area also 20 square centimetres? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the area of a 7 cm by 4 cm rectangle.1 mark
7×4=28.
28 square centimetres. - Find the area of a 12 m by 3 m rectangle.1 mark
12×3=36.
36 square metres. - Find the area of a square with side 9 cm.1 mark
9×9=81.
81 square centimetres. - A grid has 5 rows and 8 columns of one-centimetre squares. Find its area.1 mark
5×8=40.
40 square centimetres. - A rectangle is 1 m long and 30 cm wide. Find its area in square centimetres.2 marks
1 m=100 cm; 100×30=3,000.
3,000 square centimetres. - A 6 cm by 4 cm rectangle has perimeter 20 cm. Is its area also 20 square centimetres? Explain.2 marks
Area=6×4=24; perimeter=6+4+6+4=20.
No. Its area is 24 square centimetres.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Decimal metric conversions; deriving rectangle area; missing dimensions; practical measurement.
Official curriculum source ↗