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

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Answer 1 · 2017-01-19T09:30:59

2 unit^3

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

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

Base area $=1/2[[(x_1*y_2)+(x_2*y_3)+(x_3*y_1)]-[(y_1*x_2)+(y_2*x_3)+(y_3*x_1)]]$

$=1/2[[(5*7)+(2*4)+(3*1)]-[(1*2)+(7*3)+(4*5)]]$
$=1/2 [(35+8+3)-(2+21+20)]$
$=1/2 (46-43)$
$=3/2 unit^2$

The volume $=1/3*3/2*4 = 2 unit^3$

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?