# The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(4 ,2 )#, and #(2 ,6 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

##### 1 Answer

Apr 9, 2016

volume

#### Explanation:

The volume of a pyramid is given by the formula:

We are given the height (

so we need to find the base.

Method 1: Use the Pythagorean Theorem to find distance between points then apply Heron's Formula for the Area.

(left as an exercise).

Method 2: Evaluate the Area of the Triangular Base as the Sum and Difference of Trapezoids:

From the relationship between the triangle and the trapezoid segments we see that the area of the base of our pyramid is

Therefore the Volume of the pyramid is