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

##### 1 Answer

Volume of the pyramid with triangular base is

#### Explanation:

Volume of triangular pyramid =

Area of triangular base =

Base

Eqn of Base =is

Slope of base

Slope

Slope of altitude

Eqn of Altitude is

Solving Eqns (1) & (2), we get coordinates of the base of the altitude.

Coordinates of base of altitude are (7,1)

Height of altitude

Area of triangular base

Area

Volume of pyramid =