0580/43 May/Jun 2025, Question 21: Area of a Sector
Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 4 marks
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The question, in short
In an equilateral triangle ABC of side 12 cm, N and P divide AC and AB in ratio 2:1 from A, with sector ANP centred at A; find the shaded area between arc NP and CB.
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Solution · 4 marks
- 1Triangle area = 1/2 × 12 × 12 × sin 60° = 62.35…
- 2AN = 2/3 × 12 = 8 cm, angle A = 60°
- 3Sector area = 60/360 × π × 8² = 33.51…
- 4Shaded area = 62.35… − 33.51… = 28.84… ≈ 28.8 cm²
Answer28.8 or 28.83 to 28.84…
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