The idea, step by step
Undo the multiplication
A rectangle area is found by multiplying its two side lengths. If the area and one side are known, division finds the other side. For area 30 square centimetres and width 5 centimetres, length=30÷5=6 centimetres.
A missing side is a length, so its unit is centimetres or metres, not square centimetres or square metres. The area unit describes the surface, while the side unit describes one direction.
Check more than the number
Multiply the found side by the known side to recover the area. This checks the operation and helps reveal an arithmetic error. The labels length and width can be exchanged without changing the area.
Area alone does not usually fix a rectangle. An area of 24 square centimetres could come from sides 6 and 4, or 8 and 3, among other possibilities. A second condition is needed to select one rectangle.
A common trap
The missing length is 8 square centimetres because the area uses square centimetres.
Instead: A side length is measured in centimetres. Only the area uses square centimetres.
See the thinking
Worked example 1
A rectangle has area 56 square centimetres and width 7 centimetres. Find its length.
- Length×7=56, so length=56÷7.
- 56÷7=8. Check 8×7=56.
Worked example 2
A rectangular garden has area 72 square metres. One side is 12 metres. Find the other side and the perimeter.
- The missing side is 72÷12=6 metres.
- Perimeter is 12+6+12+6=36 metres.
Check your understanding
Area is 45 square metres and one side is 9 metres. Find the other side.
Show answer
5 m.
45÷9=5, and 9×5=45.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- A rectangle has area 24 square centimetres and width 4 cm. Find its length.1 mark
- A rectangle has area 63 square metres and length 9 m. Find its width.1 mark
- A rectangle has area 100 square centimetres and width 5 cm. Find its length.1 mark
- Give two different whole-number side pairs for a rectangle of area 36 square centimetres.2 marks
- A 48-square-metre garden has width 6 m. Find its length and perimeter.2 marks
- A rectangle has area 42 square centimetres and one side of 7 cm. A learner calculates 42−7 to find the other side. Explain the error and find the correct side length.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A rectangle has area 24 square centimetres and width 4 cm. Find its length.1 mark
24÷4=6.
6 cm. - A rectangle has area 63 square metres and length 9 m. Find its width.1 mark
63÷9=7.
7 m. - A rectangle has area 100 square centimetres and width 5 cm. Find its length.1 mark
100÷5=20.
20 cm. - Give two different whole-number side pairs for a rectangle of area 36 square centimetres.2 marks
Both products equal 36. Other valid pairs are acceptable.
For example, 9 cm by 4 cm and 12 cm by 3 cm. - A 48-square-metre garden has width 6 m. Find its length and perimeter.2 marks
48÷6=8; 8+6+8+6=28.
Length 8 m; perimeter 28 m. - A rectangle has area 42 square centimetres and one side of 7 cm. A learner calculates 42−7 to find the other side. Explain the error and find the correct side length.2 marks
The area formula multiplies the side lengths, so division, not subtraction, undoes it.
Divide 42 by 7 to get 6 cm.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Decimal metric conversions; deriving rectangle area; missing dimensions; practical measurement.
Official curriculum source ↗