Question

The base of a triangular pyramid is a triangle with corners at `(1 ,2 )`, `(3 ,6 )`, and `(8 ,5 )`. If the pyramid has a height of `5`, what is the pyramid's volume?

Answer 1

55 cu unit

Explanation:

We know the area of a triangle whose vertices are A(x1,y1), B(x2,y2) and C(x3,y3) is`1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]`. Here area of triangle whose vertices are (1,2), (3,6) and (8,5) is
#= 1/2[1(6-5)+3(5-2)+8(2-6)] = 1/2[1.1+3.3+8(-4)] = 1/2[1+9-32] = 1/2[-22] = -11 sq unit#
area cannot be negative. so area is 11 sq unit.
Now volume of Pyramid = area of triangle * height cu unit
= 11 * 5 = 55 cu unit