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]