# The base of a triangular pyramid is a triangle with corners at #(8 ,5 )#, #(6 ,2 )#, and #(5 ,9 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

##### 1 Answer

The volume is

#### Explanation:

The volume is the area of the base multiplied by the height:

Because we are given 3 points, the area is best computed using a determinant.

Here is a reference for the determinant that will help to compute the area given 3 points:

Substituting in the 3 points:

If find it easier to demonstrate the evaluation of a

Multiply each of the major diagonals and add them:

Multiply the minor diagonals and subtract them from the sum of the major diagonals:

Because the area cannot be negative, we choose the negative value for the

Using the