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0580/31 May/Jun 2023, Question 10: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 7 marks

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The question, in short

For a right-angled triangle with AC = 8.9 cm and BC = 13.2 cm, plus a semicircle of radius 4.5 cm on AB, find the shaded region's area and the length AB.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 5 marks

Calculate the shaded area, the part of the triangle outside the semicircle, and state its units.

  1. 1Area of triangle = 1/2 × 8.9 × 13.2 = 58.74
  2. 2Area of semicircle = 1/2 × π × 4.5² = 31.808…
  3. 3Shaded area = 58.74 − 31.808… = 26.93…
  4. 4≈ 26.9 cm²

Answer26.9 or 26.92 to 26.93 cm²

Part (b) · 2 marks

Calculate the length of side AB.

  1. 1AB² = 8.9² + 13.2²
  2. 2AB² = 79.21 + 174.24 = 253.45
  3. 3AB = √253.45 = 15.92… ≈ 15.9 cm

Answer15.9 or 15.92…

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Also searched as: 0580/31/M/J/23 · 0580_s23_qp_31 · 0580 s23 31 · question 10.
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