0580/21 Oct/Nov 2023, Question 22: Composite Perimeter, Area and Volume
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks
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The question, in short
Find the shaded area inside rhombus ABCD with side 13.6 cm and angle ABC = 41°, using sectors BAC centred at B and DAC centred at D.
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Solution · 4 marks
- 1Area of triangle ABC = 1/2 × 13.6² × sin 41 = 60.67…
- 2Sector BAC = 41/360 × π × 13.6² = 66.17…
- 3Rhombus = 2 × 60.67… = 121.34…; unshaded region between arcs = 2 × (66.17… − 60.67…) = 11.01…
- 4Shaded area = 2 × (2 × 60.67… − 66.17…) = 110.3… ≈ 110 cm²
Answer110 or 110.3…
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