The base of a triangular pyramid is a triangle with corners at $(6 ,7 )$ , $(4 ,5 )$ , and $(8 ,4 )$ . If the pyramid has a height of $6$ , what is the pyramid's volume?

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Answer 1 · 2016-03-23T21:07:52

$10$ [cubic units]

Area of the pyramid's base

$S_(base)=(1/2)|[[6,7,1],[4,5,1],[8,4,1]]|$
$S_(base)=(1/2)|30+56+16-(40+28+24)|=(1/2)|102-92|=5$

Volume of the pyramid
: $V=(S_(base)*height)/3$
$V=(5*6)/3=10$ [cubic units]

The base of a triangular pyramid is a triangle with corners at (6 ,7 )(6 ,7 ), (4 ,5 )(4 ,5 ), and (8 ,4 )(8 ,4 ). If the pyramid has a height of 6 6 , what is the pyramid's volume?