4MA1/1HR Jun 2020, Question 22: Area of a Triangle Using Sine
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
Regular octagon ABCDEFGH has 10 cm sides; find the area of shaded region ACDEH to the nearest cm².
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Split the octagon into 8 triangles from the centre; each has height 5 × tan 67.5° = 12.07 cm.
- 2Octagon area = 8 × ½ × 10 × 12.07 = 482.84 cm²
- 3Triangle ABC = ½ × 10 × 10 × sin 135° = 35.36 cm²
- 4Trapezium EFGH: HE = 10 + 2 × 10 cos 45° = 24.14, height = 10 sin 45° = 7.07, area = ½ × (10 + 24.14) × 7.07 = 120.71 cm²
- 5Shaded area = 482.84 − 35.36 − 120.71 = 326.77, so 327
Answer327
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