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A prism is a polyhedron shape with two parallel sides that are equal in length called bases and the lateral sides of a parallelogram are named as parallelograms. Here, are some major elements of a Prism that are necessary to remember.

• Bases – Two parallel and equal sides are named as bases
• Lateral Sides – The sides that will link the bases are named as lateral sides.
• Height – The distance between the two bases will be named as height.
• Refraction Surface – The two interfaces inclined at the angle of apex angle and result in refraction within a prism. The angle between two refracting surfaces is termed as the apical angle. This angle is the apex of a prism.
• Reflecting Surface – When rays hit the second refracting surface inside prism then reflection occurs and it is termed as reflecting prism here.

The Prism may be either regular and irregular in shape. For the regular prism, polygons are regular. At the same time, the irregular polygon will result in an irregular prism. There are different types of Prism popular in the mathematical world. These are – triangular prism, Square prism, Pentagon Prism, or Hexagon Prism etc. they are named based on the bases of a polygon.

• Any prism with two parallel rectangular bases and four rectangular faces then it will be named as the Rectangular Prism.
• Any prism with two parallel triangular bases and three rectangular faces then it will be named as the Triangular Prism.
• Any prism with five rectangular faces and two parallel pentagonal bases then it will be named as the Pentagonal Prism.
• Any prism with two parallel hexagonal bases and six rectangular faces then it will be named as the Hexagonal Prism.

## Prism Formula

Prism has different meanings in mathematics and optics. In mathematics, A prism is a polyhedron shape with two parallel sides that are equal in length called bases and the lateral sides of a parallelogram are named as parallelograms.

In optics, a prism is the transparent optical element with flat surfaces that will refract the light. The bases of two polygons will be connected together through lateral faces and they are mostly rectangular in shape. It may be named as Parallelogram at some places.

$\large Surface\;area\;of\;a\;prism=\left(2\times Base Area\right)+Lateral\;Surface\;Area$

$\large Volume\;of\;a\;prism= Base\; Area \times Height$

$\large Base\;Area\;of\;a\;Rectangular\;Prism=bl$

$\large Surface\;area\;of\;a\;Rectangular\;Prism=2(bl+lh+hb)$

$\large Volume\;of\;a\;Rectangular\;Prism=lbh$

Where,
b – base length of the rectangular prism.
l – base width of the rectangular prism.
h – height of the rectangular prism.

$\large Base\;area\;of\;a\;Triangular\;Prism=12ab$

$\large Surface\;area\;of\;a\;Triangular\;Prism=ab+3bh$

$\large Volume\;of\;a\;Triangular\;Prism=\frac{1}{2}\;abh$

Where,
a – apothem length of the triangular prism.
b – base length of the triangular prism.
h – height of the triangular prism.

$\large Base\;Area\;of\;Pentagonal\;Prism=\frac{5}{2}\:ab$

$\large Surface\;area\;of\;a\;Pentagonal\;Prism=5ab+5bh$

$\large Volume\;of\;a\;Pentagonal\;Prism=\frac{5}{2}\:abh$

Where,
a – apothem length of the pentagonal prism.
b – base length of the pentagonal prism.
h – height of the pentagonal prism.

$\large Base\;area\;of\;hexagonal\;prism=3ab$

$\large Surface\;area\;of\;a\;Hexagonal\;Prism=6ab+6bh$

$\large Volume\;of\;a\;Hexagonal\;Prism=3abh$

Where,
a – apothem length of the hexagonal prism.
b – base length of the hexagonal prism.
h – height of the hexagonal prism.

### Surface Area of a Rectangular Prism Formula

The surface area of a Rectangular Prism would be the sum of the area of lateral faces and its rectangular bases. The surface area is usually measured in square units.

$\large Surface\;Area\;of\;a\;Rectangular\;Prism=2(bl+lh+hb)$

Where,
b – base length of the rectangular prism.
l – base width of the rectangular prism.
h – height of the rectangular prism.

### The Volume of a Rectangular Prism Formula

The Volume is the three-dimensional space occupied by an object and it is measured in cubic units.

$\large Volume\;of\;a\;Rectangular\;Prism=lbh$

Where,
b – base length of the rectangular prism.
l – base width of the rectangular prism.
h – height of the rectangular prism.