Question

The base of a triangular pyramid is a triangle with corners at `(1 ,4 )`, `(6 ,2 )`, and `(8 ,5 )`. If the pyramid has a height of `7`, what is the pyramid's volume?

Answer 1

`color (orange)("Volume of Pyramid " V_p = (1/3) A_t * h = 70/3 " cub. units"`

Explanation:

`A (1,4), B(6,2), C(8,5), h = 7`

`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) |1 (6-8) + 6 (5-4) + 8 (4-2)| = 10`

`color (orange)("Volume of Pyramid " V_p = (1/3) A_t * h = (1/3) * 10 * 7 = 70/3 " cub. units"`