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

#V=42 2/3# units.

Explanation:

The volume of a pyramid is #V=B*h#, where #B# is the area of the base, and #h# is the height of the pyramid.

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 #1/2*4*4=8#.
The top right triangle has an area of #1/2*1*7=3.5#.
The bottom left triangle has an area of #1/2*3*5=7.5#.

The sum of the areas of these 3 triangles is #8+3.5+7.5=19#. The area of the rectangle is #5*7=35#. So, the area of the base of the pyramid is #35-19=16#.

Plugging this into the formula for the volume, we have #V=1/3*16*8=128/3=42 2/3# units.