The base of a triangular pyramid is a triangle with corners at $(6 ,2 )$ , $(3 ,1 )$ , and $(4 ,2 )$ . If the pyramid has a height of $8$ , what is the pyramid's volume?

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Answer 1 · 2016-03-13T09:48:03

Volume $V=1/3*Ah=1/3*1*8=8/3=2 2/3$

Let $P_1(6, 2)$ , and $P_2(4, 2)$ ,and $P_3(3, 1)$

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

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

$A=1/2[(6,4,3,6),(2,2,1,2)]$

$A=1/2(6*2+4*1+3*2-2*4-2*3-1*6)$

$A=1/2(12+4+6-8-6-6)$

$A=1$

Volume $V=1/3*Ah=1/3*1*8=8/3=2 2/3$

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

The base of a triangular pyramid is a triangle with corners at (6 ,2 )(6 ,2 ), (3 ,1 )(3 ,1 ), and (4 ,2 )(4 ,2 ). If the pyramid has a height of 8 8 , what is the pyramid's volume?