Prisms

Definition

A prism is a polyhedron with two congruent, parallel polygonal bases and lateral faces that are parallelograms.

Prisms represent standard geometry for structural beams, building blocks, and optical components that disperse light (refraction).

Lateral Area ( $L$ ): For a right prism, the lateral area is the product of the perimeter of the base ( $P$ $P$ ) and the height ( $h$ $h$ ): $L = Ph$ $L = P h$ .
- How to read: “The lateral area L is equal to the perimeter P times the height h.”
- Meaning: Area of all side faces combined, excluding the top and bottom bases.
Total Surface Area ( $S$ ): The sum of the lateral area and twice the base area ( $B$ $B$ ): $S = L + 2B$ $S = L + 2 B$ .
- How to read: “The total surface area S is equal to the lateral area L plus two times the base area B.”
- Meaning: Total outer surface area of the prism.
Volume ( $V$ ): The product of the base area ( $B$ $B$ ) and the height ( $h$ $h$ ): $V = Bh$ $V = B h$ .
- How to read: “The volume V is equal to the base area B times the height h.”
- Meaning: Total space enclosed by the prism.