The base of a triangular pyramid is a triangle with corners at $(3 ,7 )$ , $(5 ,4 )$ , and $(8 ,2 )$ . If the pyramid has a height of $2$ , what is the pyramid's volume?

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Answer 1 · 2017-09-22T11:58:28

Volume of a pyramid is $1 2/3$ cubic.unit [Ans]

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

the corners of base triangle are given as well as height also.

$(x_1,y_1)=(3,7) ,(x_2,y_2)=(5,4),(x_3,y_3)=(8,2) , h=2$

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

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

$A_b = |1/2(6-25+24)| = | 5/2| =5/2 =2.5$ sq.unit

Volume of a pyramid is $1/3*A_b*h = 1/3 *2.5*2 = 5/3 = 1 2/3$

cubic.unit [Ans]

The base of a triangular pyramid is a triangle with corners at (3 ,7 )(3 ,7 ), (5 ,4 )(5 ,4 ), and (8 ,2 )(8 ,2 ). If the pyramid has a height of 2 2 , what is the pyramid's volume?