1. ## SAT pyramid problem

Before i start, there is a pyramid with vertex V and altitude h and edge of e and the edge of the base is m.

NOTE: FIGURE NOT DRAWN TO SCALE.
The pyramid shown above has an altitude h and a square base of side m. The four edges that meet at V, the vertex or the pyramid, each have length e. If e=m, what is the value of h in terms of m? Answer: M times [square root of 2]

The base is a square with sides of length m so drawing a diagonal divides the square into two right triangles with leg lengths m. By the Pythagorean theorem, the diagonal has length d given by $d^2= m^2+ m^2= 2m^2$ so that $d= m\sqrt{2}$. If you drop a perpendicular from the top of the pyramid to the center of the base you have a right triangle with one leg of length h, one leg of length [tex]m\sqrt{2}/2[/itex] (half of a diagonal) and hypotenuse of length e. Put those into the Pythagorean theorem.