# 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?

We know the area of a triangle whose vertices are A(x1,y1), B(x2,y2) and C(x3,y3) is$\frac{1}{2} \left[x 1 \left(y 2 - y 3\right) + x 2 \left(y 3 - y 1\right) + x 3 \left(y 1 - y 2\right)\right]$. 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