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=4223 units.

Explanation:

The volume of a pyramid is V=Bh, 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 1244=8.
The top right triangle has an area of 1217=3.5.
The bottom left triangle has an area of 1235=7.5.

The sum of the areas of these 3 triangles is 8+3.5+7.5=19. The area of the rectangle is 57=35. So, the area of the base of the pyramid is 3519=16.

Plugging this into the formula for the volume, we have V=13168=1283=4223 units.