What Is a Prism?

How a prism is built

The most important structural idea is that a prism keeps the same cross section all the way along its length when sliced parallel to the bases. That is why prism volume is built from base area times height.

This page keeps the bases, side faces, and vertical measurement together so prism is read as a solid built from a repeated base shape rather than as a random boxlike sketch.

A triangular prism and a rectangular prism look different because their bases differ, but both follow the same structural idea. If the base area is 12 square units and the perpendicular distance between bases is 5 units, the volume is 60 cubic units.

• A prism is a polyhedron with two congruent parallel bases joined by rectangles or parallelograms.
• The two bases of a prism are congruent and lie in parallel planes.
• The height of a prism is the perpendicular distance between the bases, not merely the length of a slanted edge.
• A cylinder can be compared with the limiting idea of a prism whose base has more and more sides.

Where prisms help

• Use prisms when finding volume and surface area of boxlike or column-shaped solids.
• Use them when comparing polyhedra with curved solids such as cylinders.
• Use prism structure in cross-section problems where the repeated base shape matters.

Prism checks to make

• Do not confuse a slanted lateral edge with the perpendicular height.
• Do not call a solid a prism unless the two bases are congruent and parallel.
• Do not ignore the shape of the base when selecting formulas for area or volume.