Prism
Formulas for Competitive Exams

What is Prism?

A polyhedron with two polygonal
bases parallel to each other is a prism. In optics, the prism is the
transparent optical element with flat polished surfaces that refract light.
Lateral faces join the two polygonal bases, and these lateral faces are mostly
rectangles. It may be a parallelogram in some cases.

There are two formulas of the prism.  

1. The
surface area of a prism = (2×BaseArea) +Lateral Surface Area

2. The
volume of a prism = Base Area× Height

Types of Prism

There are different types of prisms. Some of them are:

1. Rectangular Prism: In a Rectangular Prism, 2 rectangular bases are
parallel to each other and 4 rectangular faces. 

The base area of a Rectangular prism = bl 

The
surface area of a Rectangular prism = 2(bl+lh+hb) 

The
volume of a Rectangular prism = lbh 

Where b=Base
length, l=base width, h=height

2. Triangular
Prism: In a Triangular Prism, there are 2 parallel triangular surfaces, 2
rectangular surfaces that are inclined to each other and 1 rectangular
base. 

The base area of a Triangular prism = (½)ab  

The surface area of a Triangular prism = ab+3bh  

The volume of a Triangular prism = (½)abh  

3. Pentagonal
Prism: In a Pentagonal Prism, 2 pentagonal surfaces are parallel to each
other and 5 rectangular surfaces that are inclined to each other. 

The base area of Pentagonal prism = (5/2)ab  

The surface area of a Pentagonal prism = 5ab+5bh  

The volume of a Pentagonal prism = (5/2)abh  

Where, a
= Apothem length, b=base length, h=height

4. Hexagonal
Prism: In a Hexagonal Prism, there are 2 hexagonal surfaces parallel to
each other and 6 rectangular surfaces that are inclined to each other. 

The base area of hexagonal prism = 3ab  

The surface area of a Hexagonal prism = 6ab+6bh  

The volume of a Hexagonal prism = 3abh  

Where, a
= Apothem length, b=base length, h=height

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