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

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Answer 1 · 2016-11-21T05:28:48

$V = 4$ $V=4" "$ cubic units

To solve for the volume of the pyramid which is
$V = \frac{1}{3} \cdot a r e a \cdot h e i g h t$ $V=1/3*area*height$

Solve for the area of the triangle first with $P_{1} (3, 4), P_{2} (5, 8), P_{3} (4, 8)$ $P_1(3, 4),P_2(5, 8),P_3(4, 8)$

the area A matrix

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

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

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

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

$A=1/2*(24+40+16-20-32-24)$

$A=1/2*(80-76)$

$A=2$

Now the volume V

$V=1/3*area*height$

$V=1/3*2*6=4$

$V=4" "$ cubic units

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

The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5,8)(5 ,8 ), (3 ,4 )(3,4)(3 ,4 ), and (4 ,8 )(4,8)(4 ,8 ). If the pyramid has a height of 6 66 , what is the pyramid's volume?