The base of a triangular pyramid is a triangle with corners at $(5 ,8 )$ , $(6 ,7 )$ , and $(2 ,3 )$ . If the pyramid has a height of $15$ , what is the pyramid's volume?

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Answer 1 · 2018-02-24T11:59:16

The volume of the pyramid is $20$ cubic units.

The volume of a pyramid is given by $1/3*$ base area $*$ height.

$(x_1,y_1)-=(5,8) ,(x_2,y_2)-=(6,7),(x_3,y_3)-=(2,3) , h=15$

Area of Triangle is

$A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|$

$A_b = |1/2(5(7−3)+6(3−8)+2(8−7))|$ or

$A_b = |1/2(20-30+2)| = | -8/2| =4$ sq.unit.

So, the volume of the pyramid is $1/3*A_b*h = 1/3 *4*15 = 20$ cubic units. [Ans]

The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5 ,8 ), (6 ,7 )(6 ,7 ), and (2 ,3 )(2 ,3 ). If the pyramid has a height of 15 15 , what is the pyramid's volume?