The base of a triangular pyramid is a triangle with corners at $(5 ,1 )$ , $(3 ,6 )$ , and $(4 ,8 )$ . If the pyramid has a height of $5$ , what is the pyramid's volume?

Question

1342 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-21T11:41:07

Volume of pyramid is $7.5$ cubic.unit.

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

$(x_1,y_1)=(5,1) ,(x_2,y_2)=(3,6),(x_3,y_3)=(4,8) , h=5$

Area of Triangle is

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

$A_b = |1/2(5(6−8)+3(8−1)+4(1−6))|$ or

$A_b = |1/2(-10+21-20)| = 1/2| -9| =9/2$ sq.unit.

Volume of pyramid is $V=1/3*A_b*h$ or

$V= 1/3*9/2*5 = 7.5$ cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (5 ,1 )(5 ,1 ), (3 ,6 )(3 ,6 ), and (4 ,8 )(4 ,8 ). If the pyramid has a height of 5 5 , what is the pyramid's volume?