4MA1/2H Jan 2021, Question 20: Area of a Triangle Using Sine
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
A regular hexagon ABCDEF has an equilateral triangle PQR cut out to leave shaded region T; P and Q lie on AB with AB = 1.5 × PQ. Given area of T is 72√3 cm², find PQ.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Let PQ = x, so AB = 1.5x
- 2Triangle area = (√3/4)x²; hexagon area = 6 × (√3/4)(1.5x)² = (27√3/8)x²
- 3Area T: (27√3/8)x² − (√3/4)x² = (25√3/8)x² = 72√3
- 4x² = 72 × 8 ÷ 25 = 23.04
- 5PQ = √23.04 = 4.8
Answer4.8
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