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?

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Answer 1 · 2018-06-10T05:19:49

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

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

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

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

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

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?