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. :