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Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

Edexcel IGCSE 4MA1 Similar Shapes: Exam Questions and Answers

Similar Shapes questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then try the 8 exam-style questions yourself and check your working against the mark scheme.

Practise similar shapes in Unit 5 →Geometry and Trigonometry revision notes

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Start with one question on similar shapes. Stuck? Take a hint. No sign-in needed.

Two shapes are similar. The lengths of the larger are 3 times the lengths of the smaller. The smaller has an area of 20 cm². Find the matching area of the larger.
Choose your answer · keys 1–4

What this topic covers

Similar Shapes worked examples

Worked example 1: Similar rectangles

Two similar rectangles measure 4 cm by 6 cm and 10 cm by x cm. Find x.

Solution

3 steps
Tip: Match corresponding sides.

Worked example 2: Area scale factor

Two similar shapes have corresponding lengths 3 cm and 7.5 cm. The smaller has area 16 cm². Find the larger area.

Solution

4 steps · 1 to fill in
Tip: Area scale factor = (length scale factor)².

Worked example 3: Volume scale factor

Two similar cones have heights 6 cm and 9 cm. The smaller has volume 40 cm³. Find the volume of the larger.

Solution

3 steps
Tip: Volume scale factor = (length scale factor)³.

Similar Shapes exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

Two rectangles are similar. The lengths of the rectangles are in the ratio 1 : 3. The smaller rectangle has area 8 cm². Work out the area of the larger rectangle.

Show the answer and mark scheme
  • M1 8 × 3²
  • A1 72 cm²

Answer: 72 cm²

Question 2 · easy · 1 mark

Two similar shapes have a linear scale factor of 5. Write down the area scale factor.

Show the answer and mark scheme
  • B1 25

Answer: 25

Question 3 · easy · 1 mark

The areas of two similar shapes are in the ratio 4 : 49. Write down the ratio of their corresponding lengths.

Show the answer and mark scheme
  • B1 2 : 7

Answer: 2 : 7

Question 4 · medium · 2 marks

Triangles A and B are similar. A side of 6 cm in A corresponds to a side of 9 cm in B. The area of A is 20 cm². Work out the area of B.

Full worked solution Free, no sign-in

  • M1 20 × (9/6)² or 20 × 2.25
  • A1 45 cm²

Answer: 45 cm²

Every question here has a full worked solution. See them all →

Question 5 · medium · 3 marks

Two similar shapes have areas 50 cm² and 162 cm². A length on the smaller shape is 10 cm. Work out the corresponding length on the larger shape.

Show the answer and mark scheme
  • M1 162 ÷ 50 (= 3.24)
  • M1 √3.24 (= 1.8)
  • A1 18 cm

Answer: 18 cm

Question 6 · medium · 3 marks

A photo measures 10 cm by 15 cm. It is enlarged to a similar photo with an area of 600 cm². Work out the dimensions of the enlarged photo.

Show the answer and mark scheme
  • M1 600 ÷ 150 (= 4)
  • M1 linear scale factor √4 = 2
  • A1 20 cm by 30 cm

Answer: 20 cm by 30 cm

Question 7 · hard · 3 marks

Two similar cylinders have surface areas of 80 cm² and 180 cm². The height of the smaller cylinder is 12 cm. Work out the height of the larger cylinder.

Show the answer and mark scheme
  • M1 180 ÷ 80 (= 2.25)
  • M1 √2.25 = 1.5
  • A1 18 cm

Answer: 18 cm

Question 8 · hard · 4 marks

In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 4 cm and DB = 6 cm. The area of triangle ADE is 12 cm². Work out the area of the trapezium DBCE.

Show the answer and mark scheme
  • B1 linear scale factor 10 ÷ 4 = 2.5
  • M1 12 × 2.5² (= 75)
  • M1 their 75 − 12
  • A1 63 cm²

Answer: 63 cm²

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise similar shapes for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test similar shapes?

Either Higher tier paper, 1H or 2H, can test similar shapes: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more similar shapes questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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