4MA1/1H Jun 2020, Question 11: Using Trigonometry and Pythagoras Together
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
An isosceles trapezium has parallel sides BC = 8.4 cm and AD = 17.6 cm and area 179.4 cm². Find angle ABC to 1 decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Symmetric trapezium: drop BX ⊥ AD, AX = (17.6 − 8.4) ÷ 2 = 4.6
- 2Area: ½ × (8.4 + 17.6) × h = 179.4, so 13h = 179.4, h = 13.8
- 3Triangle ABX: tan ABX = 4.6 ÷ 13.8, so ABX = 18.43…°
- 4BC ∥ AD and BX ⊥ AD, so angle XBC = 90°
- 5Angle ABC = 90° + 18.43…° = 108.4
Answer108.4
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