# The base of a triangular pyramid is a triangle with corners at #(2 ,1 )#, #(3 ,6 )#, and #(4 ,8 )#. If the pyramid has a height of #5 #, what is the pyramid's volume?

##### 1 Answer

#### Explanation:

The volume of a pyramid is given by the formula

We are given the height

so the problem is essentially finding the area of the triangular base.

The most direct way of finding the area of a triangle from its coordinates

**the absolute value** of the determinate

using the coordinates given:

making the determinant simpler by row operations

expanding by

So the area of the triangle is