The base of a triangular pyramid is a triangle with corners at #(1 ,2 )#, #(3 ,7 )#, and #(5 ,9 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

1 Answer
Nityananda
Nov 19, 2016

48 cu units

Explanation:

We know the area of a triangle whose corners are A(x1,y1), B(x2,y2) and C(x3,y3) is#1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2) sq unit#
here (x1,y1) = (1,2), (x2,y2) = (3,7) and (x3,y3) = (5,9). So area will be
#1/2[1(7-9)+3(9-2)+5(2-7)] = [1(-2)+3.7+5(-5)] = -2+21-25= -6#Area cannot be negative. Hence area will be 6 sq units.
Now volume of Pyramid = Area of triangle * height of pyramid
= 6*8 = 48 cu units

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