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0580/33 May/Jun 2024, Question 8: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

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The question, in short

Work with area and perimeter formulas for a trapezium, triangle, circle and a rectangle with two semicircles removed, finding the requested lengths and areas.

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

Part (a) · 2 marks

Use the trapezium's parallel sides 8.2 cm and 12.6 cm with perpendicular height 5.4 cm to find its area.

  1. 1Area = (8.2 + 12.6)/2 × 5.4
  2. 2= 10.4 × 5.4 = 56.16 cm²

Answer56.2 or 56.16

Part (b) · 2 marks

Given the triangle's area 15.3 cm² and perpendicular height 4.5 cm, find the base b in cm.

  1. 11/2 × 4.5 × b = 15.3
  2. 22.25b = 15.3 → b = 6.8

Answer6.8

Part (c) · 2 marks

Given a circle's circumference 58.6 cm, find its radius.

  1. 12πr = 58.6
  2. 2r = 58.6 ÷ (2π) = 9.326… ≈ 9.33 cm

Answer9.33 or 9.325 to 9.327

Part (d) · 4 marks

Find the shaded area of a 28 cm by 12 cm rectangle after removing two semicircles of diameter 12 cm.

  1. 1Rectangle = 28 × 12 = 336 cm²
  2. 2Two semicircles of radius 6 make one circle: π × 6² = 113.09… cm²
  3. 3Shaded area = 336 − 113.09… = 222.90… ≈ 223 cm²

Answer223 or 222.8 to 222.91

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