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?

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Answer 1 · 2018-06-10T05:15:36

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

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

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

$A_t = |(1/2) (2 (3-2) + 5 (2-6) + 8 (6 - 3))| = 42$

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

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