The base of a triangular pyramid is a triangle with corners at (2 ,2 ), (3 ,1 ), and (7 ,5 ). If the pyramid has a height of 6 , what is the pyramid's volume?

1 Answer
Mar 2, 2016

8

Explanation:

To find volume of a triangular pyramid of height 6 and base a triangle with corners at A(2,2), B(3,1), and C(7,5) we must find the area of the base triangle.

The sides of triangle can be found as follows.

AB=sqrt((3-2)^2+(1-2)^2)=sqrt2=1.4142

BC=sqrt((7-3)^2+(5-1)^2)=sqrt(16+16)=sqrt32=5.6568

CA=sqrt((7-2)^2+(5-2)^2)=sqrt(25+9)=sqrt34=5.831

Using Heron's formula s=(1.4142+5.6568+5.831)/2=6.451

and area of triangle is sqrt(6.451xx(6.451-1.4142)xx(6.451-5.6568)xx(6.451-5.831)
i.e. sqrt(6.451xx5.0368xx0.7942xx0.62)=4 (approx.)

As volume of pyramid 1/3xxheightxxarea of base, it is 1/3xx4xx6=8