The base of a triangular pyramid is a triangle with corners at $(5, 1)$ $(5 ,1 )$ , $(2, 7)$ $(2 ,7 )$ , and $(3, 4)$ $(3 ,4 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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The base of a triangular pyramid is a triangle with corners at $(5, 1)$ $(5 ,1 )$ , $(2, 7)$ $(2 ,7 )$ , and $(3, 4)$ $(3 ,4 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

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Answer 1 · 2017-01-19T09:30:59

2 unit^3

Explanation:

Volume of pyramid #=1/3 x base area x height

Let $x_{1} = 5, x_{2} = 2, x_{3} = 3, y_{1} = 1, y_{2} = 7 and y_{3} = 4$ $x_1=5, x_2=2,x_3=3, y_1=1,y_2=7 and y_3=4$

Base area $= \frac{1}{2} [[(x_{1} \cdot y_{2}) + (x_{2} \cdot y_{3}) + (x_{3} \cdot y_{1})] - [(y_{1} \cdot x_{2}) + (y_{2} \cdot x_{3}) + (y_{3} \cdot x_{1})]]$ $=1/2[[(x_1*y_2)+(x_2*y_3)+(x_3*y_1)]-[(y_1*x_2)+(y_2*x_3)+(y_3*x_1)]]$

$= \frac{1}{2} [[(5 \cdot 7) + (2 \cdot 4) + (3 \cdot 1)] - [(1 \cdot 2) + (7 \cdot 3) + (4 \cdot 5)]]$ $=1/2[[(5*7)+(2*4)+(3*1)]-[(1*2)+(7*3)+(4*5)]]$
$= \frac{1}{2} [(35 + 8 + 3) - (2 + 21 + 20)]$ $=1/2 [(35+8+3)-(2+21+20)]$
$= \frac{1}{2} (46 - 43)$ $=1/2 (46-43)$
$= \frac{3}{2} u n i t^{2}$ $=3/2 unit^2$

The volume $= \frac{1}{3} \cdot \frac{3}{2} \cdot 4 = 2 u n i t^{3}$ $=1/3*3/2*4 = 2 unit^3$

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The base of a triangular pyramid is a triangle with corners at $(5, 1)$ $(5 ,1 )$ , $(2, 7)$ $(2 ,7 )$ , and $(3, 4)$ $(3 ,4 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?

1 Answer

Explanation:

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The base of a triangular pyramid is a triangle with corners at (5,1)(5 ,1 ), (2,7)(2 ,7 ), and (3,4)(3 ,4 ). If the pyramid has a height of 44 , what is the pyramid's volume?

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Explanation:

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The base of a triangular pyramid is a triangle with corners at $(5, 1)$ $(5 ,1 )$ , $(2, 7)$ $(2 ,7 )$ , and $(3, 4)$ $(3 ,4 )$ . If the pyramid has a height of $4$ $4$ , what is the pyramid's volume?