# The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,5 )#, and #(4 ,2 )#. If the pyramid has a height of #9 #, what is the pyramid's volume?

##### 2 Answers

The volume is

#### Explanation:

This answer is basically in two parts:

Part 1 -- area of the triangular base is half of any side times the height from that side to the opposite vertex.

Part 2 -- vume of the pyramid is one-third the area of the base times the height.

Now to the math.

Part 1 -- it helps to draw out the triangle on graph paper. Note that the first and third vertices are both on the horizontal line

Part 2 -- The area of the base is

**Volume of pyramid is**

#### Explanation:

Vertices of triangular base are

The area of the triangular base is

Volume of pyramid is