The base of a triangular pyramid is a triangle with corners at $(7 ,7 )$ , $(5 ,3 )$ , and $(8 ,4 )$ . If the pyramid has a height of $6$ , what is the pyramid's volume?

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Answer 1 · 2016-03-14T12:16:49

Volume $V=10" "$ cubic units

Let $P_1(7, 7)$ , and $P_2(5, 3)$ ,and $P_3(8, 4)$

Compute the area of the base of the pyramid
$A=1/2[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]$

$A=1/2[x_1y_2+x_2y_3+x_3y_1-x_2y_1-x_3y_2-x_1y_3]$

$A=1/2[(7,5,8,7),(7,3,4,7)]$

$A=1/2(7*3+5*4+8*7-5*7-8*3-7*4)$

$A=1/2(21+20+56-35-24-28)$

$A=1/2(97-87)$

$A=5$

Volume $V=1/3*Ah=1/3*5*6=30/3=10$

God bless....I hope the explanation is useful.

The base of a triangular pyramid is a triangle with corners at (7 ,7 )(7 ,7 ), (5 ,3 )(5 ,3 ), and (8 ,4 )(8 ,4 ). If the pyramid has a height of 6 6 , what is the pyramid's volume?