To find the volume, we need the height of the entire pyramid, not the
slant height of the lateral faces. If the slant height is the
hypotenuse, the bottom leg is 10 meters and the Pythagorean theorem will
give us the rest.

a^{2} + b^{2} = c^{2} (10 m)^{2} + h^{2} = (14.14 m)^{2} h = 10 m

Armed with the height, we're fully equipped to calculate the volume of this pyramidal puppy.

V ≈ 1333 m^{3}

The sweet smell of success.

Example 2

Find the volume of the regular (but not right) pentagonal pyramid.

The pyramid might be oblique, but we don't treat it any differently. We still use the same formula, only this time finding the area of the base might be a bit trickier.

Splitting up the pentagon into five identical triangles should do the job. Then, we can calculate the area of each triangle and multiply it by 5.

B = 37.5 ft^{2}

Plug that guy into our volume equation and that's all there is to it.