The base of a triangular pyramid is a triangle with corners at #(5 ,1 )#, #(3 ,6 )#, and #(4 ,8 )#. If the pyramid has a height of #5 #, what is the pyramid's volume?

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Answer 1 · 2018-03-21T11:41:07

Volume of pyramid is #7.5 # cubic.unit.

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

#(x_1,y_1)=(5,1) ,(x_2,y_2)=(3,6),(x_3,y_3)=(4,8) , h=5#

Area of Triangle is

#A_b = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|#

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

#A_b = |1/2(-10+21-20)| = 1/2| -9| =9/2# sq.unit.

Volume of pyramid is #V=1/3*A_b*h # or

#V= 1/3*9/2*5 = 7.5 # cubic.unit [Ans]