E-Lecture - Surface Area and Volume of Prisms

A prism is any three dimensional geometric figure which has a uniform cross-section. A cross-section of the figure is parallel to the base such that the resulting figure has the same shape and size as that of the base of the figure. The cross-section can be triangular, rectangular, pentagonal, hexagonal, circular or combinations of shapes.

Prisms are named by the shape of the base. If the base is,
1. Triangular it is called triangular prism.
2. Rectangular it is called rectangular prism (or Cuboids).
3. Parallelogram it is called Parallelepiped.
4. A square it is called a cube or square prism.
5. Circular it is called cylinder.
6. Pentagonal it is called pentagonal prism.
7. Hexagonal it is called hexagonal prism.

Prisms: The sides of the base are said to be edges of the base. The lateral edges and edges of the base are said to be edges of the prism. The height of the prism is the distance between the bases. Prisms are classified as right prisms and oblique prisms.

A Right prism is a prism whose lateral edges are perpendicular to the bases.

An oblique prisms is a prism whose lateral edges are not perpendicular to the bases.

Base area AB of a prism is the area of the polygon which is the base of the prism. Lateral surface area AL of a prism is the sum of the areas of the lateral faces.
Therefore, the total surface area AT of a prism and its volume V are given by,

AT = AB + AL
V = hAB, where h is the height of the prism.