Question

The height of a square pyramid with a that has 12 cm edges and a lateral area of 240cm sq.

Answer 1

The height of the pyramid = 8 cm

Explanation:

Given that,

The edges of a pyramid, a = 12 cm

The lateral area of a pyramid, A = 240 cm²

The formula for the lateral area of a square pyramid is given by :

`A=a√(a^2+4h^2)`

Where

h is the height

Squaring both sides,

`A^2=a^2* (a^2+4h^2)\\\\(A^2)/(a^2)=a^2+4h^2\\\\(A^2)/(a^2)-a^2=4h^2\\\\4h^2=((240)^2)/(12^2)-12^2\\\\4h^2=256\\\\h^2=64\\\\h = 8\ cm`

So, the height of the pyramid is equal to 8 cm.