The base of a triangular pyramid is a triangle with corners at $(6 ,2 )$ , $(1 ,7 )$ , and $(5 ,4 )$ . If the pyramid has a height of $8$ , what is the pyramid's volume?

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Answer 1 · 2016-03-13T01:41:13

Volume $V=20/3" "$ cubic units

Compute the area of the triangular base:

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

$A=1/2(x_1y_2+x_2y_3+x_3y_1-x_2y_1+x_3y_2+x_1y_3)$

Let
$P_1(6,2)$
$P_2(5, 4)$
$P_3(1,7)$

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

$A=1/2[6*4+5*7+1*2-5*2-1*4-6*7]$

$A=1/2(24+35+2-10-4-42)$

$A=1/2(61-56)$
$A=5/2$

Now compute the volume of the Pyramid

$V=1/3*A*h=1/3*5/2*8$

$V=20/3" "$ 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 ), (1 ,7 )(1 ,7 ), and (5 ,4 )(5 ,4 ). If the pyramid has a height of 8 8 , what is the pyramid's volume?