Properties of Pyramids
Rule

Volume of a Pyramid

The volume of a pyramid is one third of the product of its base area and height.
Base and height of a pyramid

The base area is the area of the polygon opposite the vertex of the pyramid, and the height is measured perpendicular to the base.

Proof

Informal Justification

Consider a pyramid and a prism that have the same base area and height.

A pyramid can be modeled as a stack of prisms. The sum of the volumes of the small prisms will be greater than the pyramid's volume. However, as the number of prisms increases and they get thinner, the sum will approximate the volume of the pyramid.

Furthermore, the ratio of the sum of the volumes of each small prism to the volume of the prism will be approximated to

Number of Layers

Therefore, the volume of a pyramid is one third of the prism with the same base area and height.

Exercises
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