The base of a triangular pyramid is a triangle with corners at $(2 ,5 )$ , $(1 ,6 )$ , and $(2 ,8 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2017-07-12T10:58:56

Volume of a pyramid is $2$ cubic unit.

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

$(x_1,y_1)=(2,5) ,(x_2,y_2)=(1,6),(x_3,y_3)=(2,8) , h=4$

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

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

$A_b = |1/2(-4+3-2)| = | -3/2| =3/2$ sq.unit

Volume of a pyramid is $1/3*A_b*h = 1/cancel3 *cancel3/2*4 = 2$ cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (2 ,5 )(2 ,5 ), (1 ,6 )(1 ,6 ), and (2 ,8 )(2 ,8 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?