The base of a triangular pyramid is a triangle with corners at $(6 ,7 )$ , $(2 ,5 )$ , and $(3 ,1 )$ . If the pyramid has a height of $5$ , what is the pyramid's volume?

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Answer 1 · 2018-01-08T05:43:12

Volume of pyramid $V_p = (1/3)( A_t * h) = color (blue)(15)$

Volume of pyramid $V_p = (1/3)( A_t * h)$
Where $A_t$ is the base area of the triangle and h is the height of the pyramid.

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Using shoelace formula,

$A_t = (1/2) [(x1 - x3)(y2 - y1) - (x1 - x2)(y3-y1)]$

$A_t = (1/2){(6-3)(5-7) - (6-2)(1-7)} = (1/2)(-6 + 24) = 9$

$V_p = (1/3) * 9 * 5 = color (blue)(15)$

The base of a triangular pyramid is a triangle with corners at (6 ,7 )(6 ,7 ), (2 ,5 )(2 ,5 ), and (3 ,1 )(3 ,1 ). If the pyramid has a height of 5 5 , what is the pyramid's volume?