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?

Guest Nov 25, 2019

#1**+1 **

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 =

18√3 units^3

CPhill Nov 26, 2019