What is the formula for working out the height of a square based pyramid using the base length of one of the faces and the length of the slanted edge?

Use the pythagorean theorem. The slanted edge will be the hypotenus, 1/2 base will be one leg(b/c the point is in the center therefore only 1/2 the distance across) , and the height will be another leg.

The ^ symbol stands for "raised to the power of"

the theorem is (A^2) + (B^2) = C^2

A and B are legs and C is the slanted edge.

Assume the edge is 5 inches long, and the whole base is 6 inches long. leaving the height as B.

A=3 b/c it is one half the base, C=5, and B is unknown

if put in the equation you will derive:

B^2=16

Find the square root of 16. = 4

There! 4 would be the answer in this equation