Question

The base of a triangular pyramid is a triangle with corners at `(3 ,4 )`, `(6 ,2 )`, and `(5 ,5 )`. If the pyramid has a height of `7`, what is the pyramid's volume?

Answer 1

`7/3` cu unit

Explanation:

We know the volume of pyramid = `1/3` * area of the base * height cu unit.
Here, the area of the base of triangle = `1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]` where the corners are (x1,y1) = (3,4), (x2,y2) = (6,2) and (x3,y3) = (5,5) respectively.
So the area of the triangle =`1/2[3(2-5)+6(5-4)+5(4-2)]`
=`1/2[3*(-3) + 6*1 + 5*2]` = `1/2 * 2` = 1 sq unit
Hence the volume of pyramid = `1/3 * 1 * 7` = `7/3` cu unit