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0580/11 May/Jun 2024, Question 25: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 11 (Core) · Calculator · 7 marks

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The question, in short

For a shape combining isosceles right triangle JKL with a semicircle on diameter JL, where JK = JL = 12.8 cm, find the total area and the perimeter.

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

Part (a) · 3 marks

Calculate the total area of the triangle and semicircle combined, using JK = JL = 12.8 cm.

  1. 1Triangle = 1/2 × 12.8 × 12.8 = 81.92 cm²
  2. 2Semicircle = 1/2 × π × (12.8 ÷ 2)² = 1/2 × π × 6.4² = 64.33… cm²
  3. 3Area = 81.92 + 64.33… = 146.25… ≈ 146 cm²

Answer146 or 146.2 to 146.3

Part (b) · 4 marks

Calculate the total perimeter of the shape, including the triangle sides and the semicircular arc.

  1. 1KL = √(12.8² + 12.8²) = 18.10… cm
  2. 2Semicircle arc = 1/2 × π × 12.8 = 20.10… cm
  3. 3Perimeter = JK + KL + arc = 12.8 + 18.10… + 20.10…
  4. 4= 51.00… ≈ 51.0 cm

Answer51.0 or 51.00 to 51.01…

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