4MA1/1H Jun 2024, Question 20: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
Sector OABC has angle AOC = 60° and the shaded segment ABC has area 38 cm²; find the perimeter of segment ABC, correct to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Segment = sector − triangle: (60/360)πr² − ½r² sin 60° = 38.
- 2r²(π/6 − √3/4) = 38, so r² = 38 ÷ 0.09059 = 419.5 and r = 20.48 cm.
- 3Arc ABC = (60/360) × 2π × 20.48 = 21.45 cm.
- 4Triangle AOC is equilateral, so chord AC = r = 20.48 cm.
- 5Perimeter = 21.45 + 20.48 = 41.9
Answer41.9
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