# The base of a triangular pyramid is a triangle with corners at #(3 ,2 )#, #(5 ,6 )#, and #(2 ,8 )#. If the pyramid has a height of #9 #, what is the pyramid's volume?

##### 1 Answer

21.0

#### Explanation:

This is a two-part problem. First we must use the “distance formula” to find the base length. Any of the “base lines” may be used, as the value of h is related to each of them. We will need the additional “base” lines to calculate h from the Pythagorean Theorem. Then we will use the formula for the volume of a triangular pyramid (different from that of a square-based pyramid) to find the volume.

*Distance Formula:*

b=

*Pyramid Base Sides:*

Using the Pythagorean Theorem to find h:

Subtracting the second equation from the first we obtain:

NOW we have our “b”, “h” and H for the triangle volume formula: