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
sankarankalyanam
Jun 10, 2018

color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = 24 " cub. units"Volume of pyramid Vp=(13)⋅At⋅h=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 A−T=∣∣∣(12)(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))∣∣∣

A_t = |(1/2) (3 (2-8) + 2 (8-8) + 9 (8-2))| = 18At=∣∣∣(12)(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 = 24Volume of pyramid Vp=(13)⋅At⋅h=(13)⋅18⋅4=24

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