The surface area of a prism is the total area of all its faces, including the two congruent bases and the rectangular sides that join them.
What Is a Prism?
Definition
A prism is a three‑dimensional solid with two parallel, congruent polygonal bases and a set of rectangular (or sometimes parallelogram) lateral faces that connect corresponding sides of the bases. The shape of the base determines the name of the prism; for example, a prism with triangular bases is called a triangular prism, while one with rectangular bases is a rectangular prism (or cuboid).
Common Types
- Triangular prism – bases are triangles.
- Rectangular prism – bases are rectangles.
- Pentagonal prism – bases are pentagons.
- Hexagonal prism – bases are hexagons.
Each type follows the same principle for computing surface area, although the specific formulas for base area will differ.
Components of Surface Area
Base Area
Every prism has two bases. The area of one base is denoted by B. Because the bases are congruent, the combined area of both bases is 2B.
Lateral Surface Area
The lateral surface area (LSA) is the sum of the areas of all the rectangular sides. If the perimeter of one base is P and the height (the distance between the two bases) is h, then the LSA can be expressed as P × h. This formula works because each lateral face is a rectangle whose width is a side of the base and whose height is the prism’s height And it works..
General Formula for Total Surface Area
The total surface area (TSA) of a prism is the sum of the base areas and the lateral surface area:
[ \text{TSA} = 2B + Ph ]
Where
- B = area of one base,
- P = perimeter of the base,
