4MA1/2HR Jun 2019, Question 19: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
Sector OAPB has centre O, angle AOB = 80° and area (25/2)π cm²; find the perimeter of the shaded segment bounded by chord AB and arc APB, to 3 significant figures.
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Solution · 6 marks
- 1Sector area: πr² × 80/360 = 25/2 π, so r² = 56.25 and r = 7.5
- 2Arc APB = 2π × 7.5 × 80/360 = 10.47…
- 3Chord AB: AB² = 7.5² + 7.5² − 2 × 7.5 × 7.5 × cos 80°, so AB = 9.64…
- 4Perimeter = 10.47… + 9.64… = 20.1
Answer20.1
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