The base of a triangular pyramid is a triangle with corners at $(5 ,8 )$ , $(4 ,1 )$ , and $(9 ,3 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2018-02-11T12:29:34

Volume of the pyramid is $22$ cubic.unit .

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

$(x_1,y_1)=(5,8) ,(x_2,y_2)=(4,1),(x_3,y_3)=(9,3) , h=4$

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

$A_b = |1/2(5(1−3)+4(3−8)+9(8−1))|$ or

$A_b = |1/2(-10-20+63)| = | 33/2| =16.5$ sq.unit.

Volume of a pyramid is $1/3*A_b*h = 1/3*33/2*4 = 22$ cubic.unit
[Ans]

The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5 ,8 ), (4 ,1 )(4 ,1 ), and (9 ,3 )(9 ,3 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?