The base of a triangular pyramid is a triangle with corners at $(7 ,5 )$ , $(3 ,2 )$ , and $(5 ,7 )$ . If the pyramid has a height of $8$ , what is the pyramid's volume?

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Answer 1 · 2017-11-18T13:24:58

$V=56/3$ .

The surface of a triangle with vertices $(0,0),(x_1,y_1)$ and $(x_2,y_2)$ is $S=1/2abs(x_1y_2-x_2y_1)$ .

Therefore, the surface of the base is
$S=1/2abs((7-3)(5-7)-(7-5)(5-2))=7$ .

The volume is $V=1/3*7*8=56/3$ .

The base of a triangular pyramid is a triangle with corners at (7 ,5 )(7 ,5 ), (3 ,2 )(3 ,2 ), and (5 ,7 )(5 ,7 ). If the pyramid has a height of 8 8 , what is the pyramid's volume?