# What is Prism?

Prisms are three-dimensional solid objects in which the two ends are identical. It is the combination of flat faces, identical bases, and equal cross-sections. The faces of the prisms are parallelograms or rectangles without bases. And the bases of the prisms could be triangle, square, rectangle, or any n-sided polygon. Ex: A pentagonal prism has two pentagonal bases and 5 rectangular faces.

### Types of Prisms Depending upon the cross-sections, the prisms are named. It is of two types, namely;

• Regular Prism: If the bases of the prism are in the shape of a regular polygon, it is called a regular prism.
• Irregular Prism: If the bases are in the shape of an irregular polygon, then the prism is called an irregular prism.

### Prism Based on Shape of Bases

• Triangular prisms.
• Square prisms.
• Rectangular prism.
• Pentagonal prisms.
• Hexagonal prisms.

#### Formulas (Surface Area & Volume)

The formulas are defined for the surface area and volume of the prism. As the prism is a three-dimensional shape, so it has both properties, i.e., surface area and volume.

### Surface Area of a Prisms

The surface area of the prism is the total area covered by the faces of the prism.

For any kind of prism, the surface area can be found using the formula;

 Surface Area of a Prism = 2(Base Area)+ (Base perimeter × height)

### The volume of a Prism

The volume of the prism is defined as the product of the base area and the prism height.

Therefore,

 The volume of Prism = Base Area × Height

For example, if you want to find the volume of a square prism, you must know the area of a square, then its volume can be calculated as follows:

The volume of a square Prism = Area of square×height

V = s2 × h cubic units

Where “s” is the side of a square.

Solved Problem

Example 1: Find the volume of a triangular prism whose area is 50 cm2 and height is 6 cm.

Solution:

Base area = 50 cm2

Height = 6 cm

We know that,

The volume of a prism = (Base area × Height) cubic units

Therefore, V = 50 ×6 = 300

Hence, the volume of a triangular prism = 300 cm3.