The base of a triangular pyramid is a triangle with corners at $(7 ,5 )$ , $(6 ,4 )$ , and $(3 ,8 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2018-06-06T11:19:40

Volume of a pyramid is $4 2/3$ cubic.unit.

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

$(x_1,y_1)=(7,5) ,(x_2,y_2)=(6,4),(x_3,y_3)=(3,8) , h=4$

Area of Triangle is

$A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|$

$A_b = |1/2(7(4−8)+6(8−5)+3(5−4))|$ or

$A_b = |1/2(-28+18+3)| = | -7/2| =7/2$ sq.unit

Volume of a pyramid is

$1/3*A_b*h=1/3 *7/2*4=14/3 = 4 2/3$ cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (7 ,5 )(7 ,5 ), (6 ,4 )(6 ,4 ), and (3 ,8 )(3 ,8 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?