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

IGCSE Maths Similar Shapes 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 3 exam-style questions yourself and check your working against the mark scheme.

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

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

  1. Scale factor \(10\div4=2.5\).
  2. \(x=6\times2.5=15\).

Answer: 15

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

  1. Length factor \(7.5\div3=2.5\).
  2. Area factor \(2.5^2=6.25\).
  3. \(16\times6.25=100\) cm².

Answer: 100 cm²

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

  1. Length factor 1.5, volume factor \(1.5^3=3.375\).
  2. \(40\times3.375=135\) cm³.

Answer: 135 cm³

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

Similar Shapes exam-style questions

Try each question before you open the answer. 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 · 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.

Show the answer and mark scheme
  • M1 20 × (9/6)² or 20 × 2.25
  • A1 45 cm²

Answer: 45 cm²

Question 3 · 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

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.

More Unit 5 topics: Geometry