Pyramid relationships A pyramid has a square base and congruent triangular faces. Let θ be...

Pyramid relationships A pyramid has a square base and congruent triangular faces. Let θ be the angle that the altitude α of a triangular face makes with the altitude y of the pyramid, and let x be the length of a side (see the figure).

(a) Express the total surface area S of the four faces in terms of α and θ.

(b) The volume V of the pyramid equals one-third the area of the base times the altitude. Express V in terms of α and θ.

EXERCISE