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.
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.
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.
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 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.