The base of a triangular pyramid is a triangle with corners at #(1 ,5 )#, #(6 ,2 )#, and #(5 ,9 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
1 Answer
Jul 2, 2017
Explanation:
The volume of a pyramid is
The area of the base can be found by subtracting triangles from a rectangle. The graph of the base is shown below.
We can subtract 3 triangles from the the rectangle.
The top left triangle has an area of
The top right triangle has an area of
The bottom left triangle has an area of
The sum of the areas of these 3 triangles is
Plugging this into the formula for the volume, we have