0580/23 May/Jun 2022, Question 20: Area of a Sector
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks
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The question, in short
A square ABCD has side k cm; M is the midpoint of AD and E lies on diagonal BD, with MDE a sector centred at D. Work out what percentage of the square is shaded.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Sector radius = MD = k/2, angle MDE = 45° (diagonal of a square)
- 2Sector area = 45/360 × π × (k/2)² = πk²/32
- 3Shaded = k² − πk²/32
- 4Percentage = 100 × (1 − π/32) = 100 × (1 − 0.0981…)
- 5= 90.18… ≈ 90.2%
Answer90.2 or 90.18…
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Also searched as: 0580/23/M/J/22 · 0580_s22_qp_23 · 0580 s22 23 · question 20.
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