volume+of+a+right+or+oblique+prism

Cavalieri's Principle
If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal area, then the two solids have equal volumes.

Oblique Prism (100 sheets of paper)

Right Rectangular Prism (100 sheets of paper)

Volumes of Oblique Prisms
An oblique prism has lateral edges that are not perpendicular to the bases. The formula for a right prism we can use on a oblique prism. If you stack a set of 100 peices of paper on top of each other you make a right rectangular prism. If you push the stack into a oblique prism the number of peices of paper does not change. Which means the volume does not chnage. Both stacks have the same number of cards, and the same amount of height. Also, because every peice of paper has the same size and shape, they have the same area. Any card in either stack represents a cross section of each prism.