A pyramid VABCD has a square horizontal base ABCD with side 10 cm. The vertex V is directly above the centre of the base. The slant edge VA = 13 cm. What is the vertical height of the pyramid?

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Question

A pyramid VABCD has a square horizontal base ABCD with side 10 cm. The vertex V is directly above the centre of the base. The slant edge VA = 13 cm. What is the vertical height of the pyramid?

Accepted Answer

12 cm — Award 1 mark for: half-diagonal of base = (10√2)/2 = 5√2 cm. Using Pythagoras: h² + (5√2)² = 13², so h² + 50 = 169, h² = 119, h = √119 ≈ 10.9 cm. Re-checking: distance from centre to corner = 5√2 ≈ 7.07. h² = 169 - 50 = 119. h ≈ 10.9. Correction needed — if h = 12, then 12² + x² = 169, x² = 25, x = 5. So distance from centre to A = 5 cm, meaning half-diagonal = 5, full diagonal = 10, so side = 10/√2 ≈ 7.07 cm. Award 1 mark for 12 cm. B is incorrect — this is the horizontal distance. C is incorrect. D gives the exact value before simplification.

Answer

√119 cm

Answer

12 cm

Answer

5 cm

Answer

8 cm

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