4MA1/2H Jan 2021, Question 22: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
Sector OBC has radius (6 + x) cm and angle 50°; OA = OD = 6 cm with A on OB, D on OC. Given sector perimeter equals twice triangle OAD perimeter, find x to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1AD² = 6² + 6² − 2 × 6 × 6 × cos 50° = 25.719…, so AD = 5.071…
- 2Perimeter of OAD = 6 + 6 + 5.071… = 17.071…
- 3Perimeter of OBC = 2(6 + x) + (50/360) × 2π(6 + x) = (6 + x)(2 + 5π/18)
- 4(6 + x) × 2.8726… = 2 × 17.071… = 34.142…
- 56 + x = 11.885…, so x = 5.89
Answer5.89
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