 # Prism Formula

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. The two polygonal bases are joined by lateral faces. The lateral faces are mostly rectangle. It may be a parallelogram in some cases. The Prism Formula in general is given as,

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

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

Prism are of different types. They are named based on the base shape of prism. The types of prism are: rectangular prism, triangular prism, pentagonal prism and hexagonal prism.

Rectangular prism: A Prism that has 2 parallel rectangular bases and 4 rectangular faces is a Rectangular Prism. The Rectangular Prism Formulas are,

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

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

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

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

Triangular Prism: A prism that has 3 rectangular faces and 2 parallel triangular bases, then it is a triangular 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.

Pentagonal Prism: A prism that has 5 rectangular faces and 2 parallel pentagonal bases is a pentagonal prism: The Pentagonal Prism Formulas are,

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

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

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

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

Hexagonal Prism: A hexagonal prism is a type of prism that has six rectangular faces and two parallel hexagonal bases. The Hexagonal Prism Formulas are,

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

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

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

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

 More topics in Prism Formulas Surface Area of a Prism Formula Volume of a Triangular Prism Formula Volume of a Rectangular Prism Formula