4MA1/1FR Jun 2023, Question 20: Composite Perimeter, Area and Volume
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · 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, rounded to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1BC = 6 cm, CA = 6 cm, angle at C is 90 degrees
- 2AB² = 6² + 6² = 36 + 36 = 72
- 3AB = √72 = 6√2 ≈ 8.485 cm
- 4Circumference of semicircle on BC: (π × 6) / 2 = 3π ≈ 9.425 cm
- 5Circumference of semicircle on CA: (π × 6) / 2 = 3π ≈ 9.425 cm
- 6Circumference of semicircle on AB: (π × 8.485) / 2 ≈ (3.1416 × 8.485) / 2 ≈ 26.65 / 2 ≈ 13.325 cm
- 7Perimeter = 9.425 + 9.425 + 13.325 = 32.175 cm
- 832.175 ≈ 32.2 cm (to one decimal place)
Answer32.2
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