Suppose PABCD is a right square pyramid with apex P and base ABCD. If PBD is an equilateral triangle with side length 6, then what is the volume of PABCD?
BD is a diagonal of the base....so.....since the base is square.....one side of the base = 6/√2
The height of the equilatreal triangle = height of the pyramid .....so....
tan 60° = height of pyramid / 3
3 tan 60° = height of pyramid
3√3 = height of pyramid
So....the volume of the pyramid =
(1/3) base area * height =
(1/3) (6/√2)^2 * 3√3 =