4MA1/2FR Jun 2024, Question 26: Using Trigonometry and Pythagoras Together
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 5 marks
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The question, in short
Find the area of a hexagon made of a trapezium and a rectangle, using trigonometry with a 30° angle and given lengths 11, 5, 4.7 and 23 cm.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Split the hexagon along FC into rectangle CDEF and trapezium ABCF
- 2Rectangle: FC = ED = 23, so area = 23 × 4.7 = 108.1
- 3Height of trapezium = 5 × sin 30° = 2.5
- 4Trapezium area = ½ × (11 + 23) × 2.5 = 42.5
- 5Total area = 108.1 + 42.5 = 150.6
Answer150.6
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