The base of a triangular pyramid is a triangle with corners at $(2 ,2 )$ , $(3 ,1 )$ , and $(7 ,3 )$ . If the pyramid has a height of $6$ , what is the pyramid's volume?

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Answer 1 · 2017-10-26T12:07:38

Volume of a pyramid is $6$ cubic.unit

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

$(x_1,y_1)=(2,2) ,(x_2,y_2)=(3,1),(x_3,y_3)=(7,3) , h=6$

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

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

$A_b = |1/2(-4+3+7)| = | 6/2| =3$ sq.unit

Volume of a pyramid is $1/3*A_b*h = 1/cancel3 *cancel3*6 = 6$

cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (2 ,2 )(2 ,2 ), (3 ,1 )(3 ,1 ), and (7 ,3 )(7 ,3 ). If the pyramid has a height of 6 6 , what is the pyramid's volume?