Question

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?

Answer 1

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