The base of a triangular pyramid is a triangle with corners at (3,9), (1,6), and (2,8). If the pyramid has a height of 4, what is the pyramid's volume?

1 Answer
Mar 18, 2016

Volume of pyramid is 0.661 units.

Explanation:

First to find area of base, let us find all the sides of base triangle.

a=(13)2+(69)2=4+9=13=3.606

b=(23)2+(89)2=1+1=2=1.414

c=(21)2+(86)2=1+4=5=2.236

Now for using Heron's formula, s=12(3.606+1.414+2.236)=7.2562=3.628

Hence, area of base triangle is

3.628×(3.6283.606)×(3.6281.414)×(3.6282.236)

= 3.628×0.022×2.214×1.392=0.496

Hence, Volume of pyramid is 13×0.496×4=0.661