Question

The base of a triangular pyramid is a triangle with corners at `(4 ,1 )`, `(3 ,1 )`, and `(9 ,5 )`. If the pyramid has a height of `8`, what is the pyramid's volume?

Answer 1

`16/3=5.33`

Explanation:

Pyramid volume `V=1/3*A*H`, where `A` is the pyramid's base area and `H` is the height of the pyramid.

Given that `A(3,1), B(4,1) and C((,5)` are the triangular base's corners, as shown in the diagram,
`=> A=1/2*1*4=2`

Given that the pyramid has a height of `8, => H=8`

`=> V=1/3AH=1/3*2*8=16/3=5.33`