VABCD is a square-based pyramid where ABCD is a horizontal square of side 10 cm and V is directly above the centre of the square. The vertical height of the pyramid is 12 cm. Calculate the length VA.

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Question

VABCD is a square-based pyramid where ABCD is a horizontal square of side 10 cm and V is directly above the centre of the square. The vertical height of the pyramid is 12 cm. Calculate the length VA.

Accepted Answer

13 cm — Award 1 mark for finding half-diagonal of base = (10√2)/2 = 5√2 cm, then VA² = 12² + (5√2)² = 144 + 50 = 194... This is incorrect. The distance from centre to corner A = √(5² + 5²) = √50. VA² = 12² + 50 = 194, VA = √194 ≈ 13.93 cm. Reconsidering: VA = √(144 + 50) = √194 ≈ 13.9 cm. B is the exact answer. A is incorrect — 13 cm would require different dimensions. C is incorrect — this uses the full diagonal instead of half. D is incorrect — this is an approximation error.

Answer

√244 cm

Answer

15.6 cm

Answer

√194 cm

Answer

13 cm

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