4024/12 Oct/Nov 2025, Question 23: Trigonometry in 3D: Pyramids and Cones
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Square-based pyramid with vertex E above base centre X, EX = 7 cm and triangle BEC height 11 cm; find the base side length as a simplified surd.
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Solution · 4 marks
- 1Let M be the midpoint of BC, so EM = 11 cm and EX = 7 cm
- 2XM² = 11² − 7² = 121 − 49 = 72
- 3XM = √72 = 6√2 cm
- 4Base length = 2 × XM = 2 × 6√2 = 12√2 cm
Answer12√2
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