Work backwards
Find a missing side from area or perimeter
A missing-side problem gives the result of a calculation and asks you to reverse it. First identify whether the given total is area or perimeter; the two routes use different inverse operations.
Grades 4–6 · worked example · 3 practice checks
01
Recognize the problem first
- If area and one side are known, divide area by the known side.
- If perimeter and one side are known, halve the perimeter first, then subtract the known side.
- Keep square units for the given area, but write the missing side in ordinary length units.
02
Work through one complete example
Question
A rectangle has area 48 cm² and length 8 cm. What is its width?
- Use area = length × width.
- Reverse the multiplication: width = area ÷ length.
- Calculate 48 ÷ 8 = 6 and label the side in centimetres.
AnswerThe width is 6 cm.
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03
Common mistakes to catch
- Multiplying 48 by 8 instead of reversing the operation.
- Writing 6 cm² even though the answer is a length.
- For a perimeter problem, subtracting one side from the full perimeter without accounting for pairs of equal sides.
0401 02 03
Try three quick checks
Area 63 cm², length 9 cm. Find the width.
Show answer
7 cmPerimeter 30 m, length 9 m. Find the width.
Show answer
6 mA square has perimeter 36 cm. Find one side.