The base of a triangular pyramid is a triangle with corners at $(3 ,4 )$ , $(6 ,2 )$ , and $(5 ,7 )$ . If the pyramid has a height of $7$ , what is the pyramid's volume?

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Answer 1 · 2016-10-14T19:30:35

The volume is $V = 91/6color(white).units^3$

The volume, V, of a triangular pyramid is:

$V =(1/3)Ah$

where A is the area of the base and h is the height.

We are given $h = 7$

$Area = |(A_x(B_y − C_y) + B_x(C_y − A_y)+ C_x(A_y − B_y))/2|$

$Area = |(3(2 − 7) + 6(7 − 4)+ 5(4 − 2))/2|$

$Area = 13/2$

$V =(1/3)(13/2)7$

$V = 91/6color(white).units^3$

The base of a triangular pyramid is a triangle with corners at (3 ,4 )(3 ,4 ), (6 ,2 )(6 ,2 ), and (5 ,7 )(5 ,7 ). If the pyramid has a height of 7 7 , what is the pyramid's volume?