Question

The base of a triangular pyramid is a triangle with corners at `(6 ,7 )`, `(2 ,5 )`, and `(3 ,1 )`. If the pyramid has a height of `5`, what is the pyramid's volume?

Answer 1

Volume of pyramid `V_p = (1/3)( A_t * h) = color (blue)(15)`

Explanation:

Volume of pyramid `V_p = (1/3)( A_t * h)`
Where `A_t` is the base area of the triangle and h is the height of the pyramid.

Using shoelace formula,

`A_t = (1/2) [(x1 - x3)(y2 - y1) - (x1 - x2)(y3-y1)]`

`A_t = (1/2){(6-3)(5-7) - (6-2)(1-7)} = (1/2)(-6 + 24) = 9`

`V_p = (1/3) * 9 * 5 = color (blue)(15)`