The base of a triangular pyramid is a triangle with corners at $(2 ,5 )$ , $(6 ,4 )$ , and $(7 ,8 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2018-01-07T10:50:12

Volume of the pyramid is $11 1/3$ cubic.unit.

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

$(x_1,y_1)=(2,5) ,(x_2,y_2)=(6,4),(x_3,y_3)=(7,8) , h=4$

Area of Triangle is

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

$A_b = |1/2(2(4−8)+6(8−5)+7(5−4))|$ or

$A_t = |1/2(-8+18+7)| = 1/2|17| =17/2$ sq.unit.

Volume of pyramid is $1/3*A_b*h = 1/3 *17/2*4 = 34/3=11 1/3$

cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (2 ,5 )(2 ,5 ), (6 ,4 )(6 ,4 ), and (7 ,8 )(7 ,8 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?