The base of a triangular pyramid is a triangle with corners at $(5 ,8 )$ , $(4 ,3 )$ , and $(9 ,4 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2017-07-10T11:44:12

Volume of pyramid is $16$ cubic unit.

$(x_1,y_1) = (5,8) ; (x_2,y_2) = (4,3) ; (x_3,y_3) = (9,4)$

Area of triangle with given vertices is $A_t=1/2(x_1(y_2-y_3) +x_2(y_3-y_1)+x_3(y_1-y_2)$ or

$A_t=1/2(5(3-4) +4(4-8)+9(8-3)) = 1/2 (-5-16+45)=1/2*24=12$ sq.unit

Given height of pyramid is $h=4$

Volume of a pyramid is $V=1/3*A_t*h= 1/3*12*4=16$ cubic unit [Ans]

The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5 ,8 ), (4 ,3 )(4 ,3 ), and (9 ,4 )(9 ,4 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?