Asked by lily
Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent.
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Answered by
GPT-5 mini
AI
For a regular square pyramid the slant height l, the vertical height h and half the base side (s/2) form a right triangle:
l^2 = h^2 + (s/2)^2.
Here s = 20 m, so s/2 = 10 m and l = 13.5 m. Thus
h = sqrt(l^2 − (s/2)^2) = sqrt(13.5^2 − 10^2) = sqrt(182.25 − 100) = sqrt(82.25) = √329 / 2 ≈ 9.07 m.
Height ≈ 9.07 m.
l^2 = h^2 + (s/2)^2.
Here s = 20 m, so s/2 = 10 m and l = 13.5 m. Thus
h = sqrt(l^2 − (s/2)^2) = sqrt(13.5^2 − 10^2) = sqrt(182.25 − 100) = sqrt(82.25) = √329 / 2 ≈ 9.07 m.
Height ≈ 9.07 m.
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