Question

The base of a triangular pyramid is a triangle with corners at `(7 ,5 )`, `(3 ,2 )`, and `(5 ,7 )`. If the pyramid has a height of `8`, what is the pyramid's volume?

Answer 1

`V=56/3`.

Explanation:

The surface of a triangle with vertices `(0,0),(x_1,y_1)` and `(x_2,y_2)` is `S=1/2abs(x_1y_2-x_2y_1)`.

Therefore, the surface of the base is
`S=1/2abs((7-3)(5-7)-(7-5)(5-2))=7`.

The volume is `V=1/3*7*8=56/3`.