How to find the height of a regular pyramid with a square base with only a given side and a given slant height?

Question

I have to find the height of a square base pyramid with two given measurements, s= 16cm, slant height= 10cm, I already found the S.A and Lateral area, which is L.a= 320 cm and S.A = 576cm, I just don’t know how I am supposed to find the height of the pyramid

Answer 1

The slant height, height and one half of the length of a side form a right triangle with the slant height as the hypotenuse, so by the Pythagorean Theorem:

half length of side ^2 + height^2 = slant height^2

8^2 + height^2 = 10^2

height = 6 cm