Question

The base of a triangular pyramid is a triangle with corners at `(3 ,8 )`, `(2 ,2 )`, and `(9 ,8 )`. If the pyramid has a height of `4`, what is the pyramid's volume?

Answer 1

`color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = 24 " cub. units"`

Explanation:

`A (3,8), B (2,2), C (9,8), h = 4`

`"Area of base triangle " A-T = |(1/2)( x_1 (y_2-y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2))|`

`A_t = |(1/2) (3 (2-8) + 2 (8-8) + 9 (8-2))| = 18`

`color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = (1/3) * 18 * 4 = 24`