The base of a triangular pyramid is a triangle with corners at $(6 ,2 )$ , $(8 ,7 )$ , and $(3 ,4 )$ . If the pyramid has a height of $8$ , what is the pyramid's volume?

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Answer 1 · 2017-12-28T11:17:55

Volume of the pyramid is 25 1/3# cubic.unit.

Volume of a pyramid is $1/3*$ base area $*$ hight.

$(x_1,y_1)=(6,2) ,(x_2,y_2)=(8,7),(x_3,y_3)=(3,4) , h=8$

Area of Triangle is $A_b = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|$

$A_b = |1/2(6(7−4)+8(4−2)+3(2−7))|$ or

$A_b = |1/2(18+16-15)| = | 19/2| =19/2$ sq.unit

Volume of the pyramid is $1/3*A_b*h = 1/3 *19/2*8 = 76/3$

$25 1/3$ cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (6 ,2 )(6 ,2 ), (8 ,7 )(8 ,7 ), and (3 ,4 )(3 ,4 ). If the pyramid has a height of 8 8 , what is the pyramid's volume?