4MA1/1HR Jun 2025, Question 25: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
Using a diagram of two sectors with centres A and C, angle BAC 40°, angle BCD 130° and shaded segment area 28 cm², find arc BD length to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Segment area: (40/360) × πr² − (1/2)r² sin 40° = 28
- 2r² (0.349066 − 0.321394) = 28, so r² = 1011.8...
- 3r = AB = AC = 31.81 cm
- 4BC = 2 × 31.81 × sin 20° = 21.76 cm (radius of sector BCD)
- 5Arc BD = (130/360) × 2π × 21.76
- 6= 49.4 cm (3 sf)
Answer49.4
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