# The base of a triangular pyramid is a triangle with corners at #(2 ,6 )#, #(5 ,3 )#, and #(8 ,7 )#. If the pyramid has a height of #18 #, what is the pyramid's volume?

##### 1 Answer

#### Explanation:

Given the vertices of the base triangle of a pyramid and altitude:

Altitude,

Required: The volume?

This problem can be solved as follows:

So the strategy is:

**a) Use distance formula to determine the length of sides of the triangle**:

Distance formula of,

Since the base is on the x-y plane

**b) Now calculate the area. Since you know all sides you can use Heron's formula**:

where

**b) Now calculate the volume. **: