The base of a triangular pyramid is a triangle with corners at $(6 ,2 )$ , $(3 ,5 )$ , and $(4 ,2 )$ . If the pyramid has a height of $8$ , what is the pyramid's volume?

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Answer 1 · 2016-06-05T02:07:56

$V=8" "$ cubic units

the volume $V$ of a triangular pyramid has the formula

Volume = 1/3 of Area of base * Height of pyramid

Let us compute the area $A$ of the base with
$P_1(x_1, y_1)=(6, 2)$
$P_2(x_2, y_2)=(3, 5)$
$P_3(x_3, y_3)=(4, 2)$

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

$A=1/2*[x_1*y_2+x_2*y_3+x_3*y_1-x_2*y_1-x_3*y_2-x_1*y_3]$

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

$A=1/2*[6*5+3*2+4*2-3*2-4*5-6*2]$

$A=1/[30+6+8-6-20-12]$

$A=1/2(44-38)$

$A=3" "$ square units

Let us now compute the volume V of the pyramid

$V=1/3*A*h$

$V=1/3*3*8$

$V=8" "$ cubic units

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 ,5 )(3 ,5 ), and (4 ,2 )(4 ,2 ). If the pyramid has a height of 8 8 , what is the pyramid's volume?