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

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Answer 1 · 2017-10-06T11:41:23

Volume of the pyramid is $9.17$ cubic.unit.

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

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

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

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

$A_b = |1/2(-20+21-12)| = | -11/2| =11/2=5.5$ sq.unit

Volume of pyramid is $1/3*A_b*h = 1/3*5.5*5 ~~9.17$ cubic unit [Ans]

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