Question

The base of a triangular pyramid is a triangle with corners at `(2 ,6 )`, `(5 ,3 )`, and `(8 ,2 )`. If the pyramid has a height of `2`, what is the pyramid's volume?

Answer 1

`color(crimson)("Volume of pyramid " V_p = (1/3) * A_t * h = 28 " cub. units"`

Explanation:

`A (2,6), B (5,3), C (8,2), h = 2`

`"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) (2 (3-2) + 5 (2-6) + 8 (6 - 3))| = 42`

`color(crimson)("Volume of pyramid " V_p = (1/3) * A_t * h = (1/3) * 42 * 2 = 28`