4MA1/1HR Jun 2023, Question 4: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Three semicircles are drawn on the sides of a right-angled triangle with BC = CA = 6 cm. Find the total perimeter of the shape, giving the answer to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Angle C is a right angle, so AB² = 6² + 6² = 72
- 2AB = √72 = 8.4853 cm
- 3The perimeter is the three semicircle arcs added together
- 4Each arc is half of π × its diameter, so the total is (π ÷ 2) × (AB + BC + CA)
- 5AB + BC + CA = 8.4853 + 6 + 6 = 20.4853
- 6(π ÷ 2) × 20.4853 = 32.178
- 7To 1 decimal place the perimeter is 32.2 cm
Answer32.2
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