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

1 Answer
Jun 10, 2018

color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = 24 " cub. units"Volume of pyramid Vp=(13)Ath=24 cub. units

Explanation:

A (3,8), B (2,2), C (9,8), h = 4A(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))|Area of base triangle AT=(12)(x1(y2y3)+x2(y3y1)+x3(y1y2))

A_t = |(1/2) (3 (2-8) + 2 (8-8) + 9 (8-2))| = 18At=(12)(3(28)+2(88)+9(82))=18

color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = (1/3) * 18 * 4 = 24Volume of pyramid Vp=(13)Ath=(13)184=24