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

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Answer 1 · 2016-03-23T09:06:03

Volume $V=11" "$ cubic units

Compute the area of the triangular base first

Area $A=1/2[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]$

Area $A=1/2*(x_1*y_2+x_2*y_3+x_3*y_1-x_2*y_1-x_3*y_2-x_1*y_3)$

The given points are $P_1(6, 7)$ , $P_2(5, 3)$ , $P_3(8, 4)$

Area $A=1/2[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]$

Area $A=1/2[(6,5,8,6),(7,3,4,7)]$

Area $A=1/2*(6*3+5*4+8*7-5*7-8*3-6*4)$

Area $A=1/2*(18+20+56-35-24-24)$

Area $A=1/2*(94-83)$

Area $A=1/2*(11)=5.5$

Compute the volume of the triangular pyramid

$V=1/3*A*h=1/3*11/2*6$

$V=11" "$ cubic units

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

The base of a triangular pyramid is a triangle with corners at (6 ,7 )(6 ,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?