The base of a triangular pyramid is a triangle with corners at $(4 ,5 )$ , $(6 ,1 )$ , and $(7 ,3 )$ . If the pyramid has a height of $15$ , what is the pyramid's volume?

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Answer 1 · 2018-01-10T10:32:58

Volume of a pyramid is $20$ cubic.unit.

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

$(x_1,y_1)=(4,5) ,(x_2,y_2)=(6,1),(x_3,y_3)=(7,3) , h=15$

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

$A_b = |1/2(4(1−3)+6(3−5)+7(5−1))|$ or

$A_b = |1/2(-8-12+28)| =1/2 *8 =4$ sq.unit.

Volume of a pyramid is $1/3*A_b*h = 1/3 *4*15 = 20$ cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (4 ,5 )(4 ,5 ), (6 ,1 )(6 ,1 ), and (7 ,3 )(7 ,3 ). If the pyramid has a height of 15 15 , what is the pyramid's volume?