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.