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The height of a square pyramid where the lateral area equals 240 cm sq. and the edges of the base are 12cm

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Answer:

The height is 8cm

Explanation:

Given


L_A = 240cm^2 --- lateral area


a = 12cm --- base lengths

Required

The height of the pyramid

The lateral area of a square pyramid is:


L_A = a\sqrt{a^2 + 4h^2

So, we have:


240 = 12\sqrt{12^2 + 4h^2


240 = 12\sqrt{144 + 4h^2

Divide both sides by 12


20 = \sqrt{144 + 4h^2

Square both sides


400 = 144 + 4h^2

Collect like terms


4h^2 = 400 - 144


4h^2 = 256

Divide by 4


h^2 = 64

Take square roots


h = 8

User Luan Fonseca
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