# Prism

A** prism **is a solid shape that is bound on all its sides by plane faces. A **prism** is a three dimensional polyhedron characterized by two bases that are polygonal in shape and rectangular sides perpendicular to the base. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases.

A prism contains two bases which are also polygonal.

Prism does not have an apex.

The faces other than the top and bottom of a prism are called its lateral faces. One of the most common examples of a prism is a cuboid. It has a rectangular base and is called a rectangular prism.

A prism can be labeled with its features, which helps characterize them.

Edge: A straight line that connects any two adjacent vertices of a prism is called its edge.

Vertex: The corners of a prism where any two edges meet are called vertices.

Face: It is a closed, flat surface surrounded by vertices and edges.

## Cross Sections of a Prism

The cross section of a prism is the shape obtained when a plane intersects a prism along its axis. Based on the shape of the base, prisms can be categorized into the following:

**Triangular prism**: The base of the prism is triangular in shape.**Hexagonal prism**: It is a prism with a base in the shape of a hexagon.**Square prism**: A prism that has a base in the shape of a square. You may have seen a square prism with a different name, it is also called a cube.**Pentagonal prism**: The base of the prism is shaped like a pentagon.**Rectangular prism**: A prism that has bases in the shape of a rectangle. A rectangular prism is also known as a cuboid.

## Right Prism and Oblique Prism

A right prism will have two flat ends and they are perfectly aligned with every side face. An oblique prism, on the other hand, will appear to be somewhat tilted with two bases that are not aligned. The side faces of such a prism are parallelograms.

**Formula Prism**

**Surface Area = (2 ✕ Base Area) + (Base perimeter ✕ Height)**

The surface area of a prism is the total area on all of its bases and faces.

**Volume of a Prism = Area of base ✕ Height**

**Types of Prism**

Prisms are of different types, which are named according to their base shape.

**Rectangular Prism :**

A Rectangular Prism has 2 parallel rectangular bases and 4 rectangular faces.

- Base Area = b×l
- Surface area = 2× (bl+lh+hb)
- Volume = l×b×h

where b-base length ; l-base width, h-height

### Triangular Prism :

A triangular prism has 3 rectangular faces and 2 parallel triangular bases.

- Base area = $\frac{1}{2}ab$
- Surface area = ab+3bh
- Volume=$\frac{1}{2}$abh

where b-base length; a-apothem length; h-height

### Pentagonal Prism :

A pentagonal prism has 5 rectangular faces and 2 parallel pentagonal bases.

- Base Area= $\frac{5}{2}$ab
- Surface area= 5ab+5bh
- Volume = $\frac{5}{2}$abh

where b-base length; a-apothem length; h-height

### Hexagonal Prism

A hexagonal prism has six rectangular faces and two parallel hexagonal bases.

- Base area= 3ab
- Surface area= 6ab+6bh
- Volume= 3abh

where b-base length; a-apothem length; h-height