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

Question

asked Apr 7, 2022 157k views

1 Answer

Luan Fonseca · Answer 1 · 2022-04-10T23:30:50+0000

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