Prisms are mathematically defined as solid objects with flat sides, identical ends and the same cross section throughout the entire length of the object. The prisms are named based on the shape we get when cutting straight through an object also known as the cross section.
Prisms do not necessarily have a fixed number of faces, vertices or edges. Vertices is the plural for vertex and it is defined as the point where two or more edges meet.
An edge is a line segment on the boundary joining one vertex to another. Each flat surface in prism is called a face.
The most common prism-shaped objects that we see in our everyday life include ice cubes, boxes, juice boxes, cereal boxes, aquariums. etc.
Types of Prisms.
There are several types of prisms and they include;
- Rectangular Prism
- Triangular Prism
- Square Prism
- Pentagonal Prisms
- Hexagonal Prisms
A rectangular prism also known as a cuboid is a 3-dimensional solid object that has six faces that are all rectangles, this is also where it gets its name from.
Rectangular prisms can be of two types, namely right rectangular prisms and non-right rectangular prisms.
The right rectangular prisms are prisms whereby the angles between the base and sides are right angles.
While the non-right rectangular prisms are prisms whose base and sides do not meet at a right angle (90 degrees).
Properties of a Rectangular Prism.
- A rectangular prism has a rectangular cross section.
- A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces.
- All the opposite faces of a rectangular prism are equal
Surface Area and Volume of a Rectangular Prism.
Since all the faces of a rectangular prism are rectangles and opposite faces are equal, the surface area of a rectangular prism can be calculated by finding the area of each of the faces and adding the area together.
Surface Area = 2 [( width x length ) + ( length x height ) + (width x height )]
Calculating the volume of a rectangular prism is pretty easy as you just multiply the three dimensions ie:
Volume = Length x Width x Height
Some of the common examples of rectangular prisms are aquariums, boxes etc.
Triangular Prism.
A triangular prism is a prism composed of two triangular bases and three rectangular sides.
Properties of a triangular prism.
- Triangular prism has a triangular cross section.
- A triangular prism has a total of 9 edges, 5 faces, and 6 vertices which are joined by the rectangular faces.
- It has two triangular bases and three rectangular sides.
- We say a triangular prism is semi-regular if its triangular bases are equilateral and the other faces are squares, instead of a rectangle.
Triangular prisms can then be classified based on how their bases and lateral faces intersect. They include:
- Right triangular prism
This is a prism whose bases are perpendicular to the lateral faces, meaning they meet at right angles.
- Oblique triangular prism.
This prism’s bases are not perpendicular to the lateral faces and do not meet at right angles.
Triangular prisms can also be categorised on the type of the triangle that forms its base. They are:
- Regular Triangular Prism.
This kind of a triangular prism has its base formed by an equilateral triangle.
- Irregular Triangular Prism.
This kind of a prism has its base formed by an irregular polygon eg. a scalene triangle.
Surface Area and Volume of a Triangular Prism.
Since the two identical faces in a triangular prism are a triangle, we calculate the volume by multiplying the area of a triangle by the height of the prism. Read more on How To Calculate.
Volume = ( ½ x Base x Height ) x Height
We calculate the surface area of the prism by finding the area of the two triangles and add it to the area of the three sides that are rectangular in shape.
Surface Area = 2 ( ½ x Base x Height ) + ( a + b + c ) x Height
a, b and c is the length of the sides making up the three rectangles.
The most common example of a triangular prism is a chocolate candy bar.
Square Prism
A square prism or commonly known as a cube is a three dimensional solid object that has six identical square faces joined along their identical sides.
Properties of a Cube.
- A cube has a square-like cross section.
- A cube has 6 faces, 8 vertices and 12 edges.
- All the faces of a cube are equal.
- All the faces intersect at 90 degrees.
Surface Area and Volume of a Cube.
Since the identical faces are squares, it is easy to calculate the surface area of the cube.
To calculate the surface area of a cube, we find the area of one of the faces and then multiply that area by the number of faces which are 6.
Surface Area = ( Side x Side) x 6
To calculate the volume of a cube, we use the following formula;
Volume = Side x Side x Side
Some of the most common examples of square prisms are sugar cubes, ice cubes and even some cakes are made in this shape.
Pentagonal Prisms.
The pentagonal prism is a prism that has a 5 sided polygon also known as a pentagon as its base and five rectangular sides.
Properties of a pentagonal prism.
- A pentagonal prism has 7 faces, 15 edges, and 10 vertices.
- The cross section of a pentagonal prism is a pentagon.
- It is made up of 5 rectangular sides and 2 pentagons.
Surface Area and Volume of a Pentagonal Prism.
To calculate the surface area of a pentagonal prism, we find the area of the 5 rectangular sides and then find the area of the two pentagons.
One of the ways to find the area of a pentagon is dividing the pentagon into five triangles, then find the area of each triangle and add them together.
You can also use the following formula.
To calculate the volume of the prism, we use the following formula;
Where a is the base edge and h is the height.
One of the most common pentagonal prisms is The Pentagon which is the headquarters of the U.S. Defense Department.
Hexagonal Prism.
The hexagonal prism is a prism that has a 6 sided polygon also known as a hexagon as its base and six rectangular sides.
Properties of a hexagonal prism.
- A hexagonal prism has 8 faces, 18 edges, and 12 vertices.
- The cross section of a hexagonal prism is a hexagon.
- It is made up of 6 rectangular sides and 2 hexagons.
Surface Area and Volume of a hexagonal prism.
To calculate the surface area of the prism, we find the area of all the rectangular sides and then add it to the area of the two hexagons.
You can also use the following formula;
Surface Area = 6ah + 3 √3a2
Where a is the base edge and h is the height.
To calculate the volume of the hexagonal prism, we use the following formula;
Some of the most common examples of real life hexagonal prisms are unsharpened pencils, bolt heads and hardware nuts.
Uses of Prisms.
- An ordinary triangular prism can separate white light into its constituent colours, called a spectrum.
- In photography, prisms are uniquely able to bend light, glares, and reflections before they enter a camera’s lens.
- Prisms are also used in the making of telescopes, periscopes and microscopes.
- Prisms are also commonly used as construction designs.
