Question 1Warm-upFoundation
Shapes A and B are similar. A side of 5 cm on A matches a side of 15 cm on B. Another side on A is 8 cm. Find the matching side on B.
Scale factor 3.
Worked solution
- cm
Answer: cm
GCSE & IGCSE maths practice
Similar shapes questions and answers
Similar shapes are enlargements of each other: the angles are the same and every length is multiplied by the same scale factor . Areas are multiplied by and volumes by . Find from a pair of matching sides, then use it.
8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where similar shapes comes up
| GCSE (AQA, Edexcel, OCR) | Foundation and Higher: congruence and similarity, including the relationships between lengths in similar figures. Higher only: areas and volumes of similar figures. |
|---|---|
| Cambridge IGCSE (0580) | Core: calculate lengths of similar shapes. Extended: the relationships between lengths, areas and volumes of similar shapes and solids. |
The method
- Find a pair of matching sides; k = new ÷ old.
- Lengths × k; areas × k²; volumes × k³.
- Given an area ratio: k = √(ratio). Given a volume ratio: k = ∛(ratio).
- Similar triangles: match the sides opposite equal angles.
Similar shapes questions
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Warm-up
Question 2Warm-upFoundation
Shape B is an enlargement of shape A with scale factor 2.5. A side on B is 10 cm. Find the matching side on A.
Divide by the scale factor.
Worked solution
- cm
Answer: cm
Exam-style
Question 3Exam-styleFoundation
In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 4 cm, AB = 10 cm and DE = 6 cm. Find BC.
Triangles ADE and ABC are similar, k = 10/4.
Worked solution
- cm
Answer: cm
Question 4Exam-styleFoundation
A 3 cm by 5 cm rectangle is similar to a 4.5 cm by cm rectangle. Find .
k = 4.5 ÷ 3.
Worked solution
Answer:
Question 5Exam-styleHigher
Two similar shapes have lengths in the ratio 1 : 3. The smaller has area 10 cm². Find the area of the larger.
Area scale factor = 3².
Worked solution
- cm²
Answer: cm²
Question 6Exam-styleHigher
Two similar solids have lengths in the ratio 1 : 2. The smaller has volume 50 cm³. Find the volume of the larger.
Volume scale factor = 2³.
Worked solution
- cm³
Answer: cm³
Challenge
Question 7ChallengeHigher
Two similar shapes have areas 20 cm² and 45 cm². A side of the smaller is 6 cm. Find the matching side of the larger.
Area factor 2.25; length factor √2.25.
Worked solution
- cm
Answer: cm
Question 8ChallengeHigher
Two similar solids have volumes 54 cm³ and 250 cm³. The smaller has surface area 36 cm². Find the surface area of the larger.
Volume factor → length factor → area factor.
Worked solution
- , so
- Area factor
- cm²
Answer: cm²
Common mistakes
- Using k (not k²) for areas.
- Matching the wrong sides.
- Adding instead of multiplying.
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Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:
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