A prism is a three-dimensional geometric shape that has similar parallel ends and consists of all flat faces. The volume of a prism can be calculated by obtaining the product of its base area and height. Similarly, the surface area of a prism is given as twice the base area plus the product of the perimeter of the base and the prism height.
Types of Prism
On the basis of the shape of the base
On the basis of the shape of identical and parallel ends of a prism, it can be broadly classified into 5 categories, namely rectangular prism, square prism, triangular prism, pentagonal prism, hexagonal prism, etc.
1. Rectangular Prism
A rectangular prism is also known as a cuboid. It consists of two congruent rectangular bases placed at an angle of 90° to each other. The edges of the rectangular bases are connected to each other with the help of four other rectangles. Thereby, forming a three-dimensional geometric shape that has all flat faces.
2. Square Prism
As the name itself suggests, the bases of a square prism are square in shape. These bases are congruent in nature and are placed parallel to each other. Four two-dimensional square faces used to connect the two parallel and congruent bases of a square prism possess similar dimensions as that of the bases. Thereby, forming a cube-geometric structure.
3. Triangular Prism
The shape of the bases of a triangular prism is a two-dimensional triangle. Three identical rectangular faces are used to connect these parallel triangular bases. A triangular prism is a pentahedron because it consists of five faces.
4. Pentagonal Prism
The shape of the base of a pentagonal prism is a five-sided polygon or a pentagon. It consists of five rectangular faces connecting the bases of the prism.
5. Hexagonal Prism
A three-dimensional geometric shape that consists of two congruent hexagonal bases placed parallel to each other connected with the help of six rectangular sides is known as a hexagonal prism.
On the basis of the cross-section
1. Regular Prism
If the shape of the cross-section of a prism is a regular polygon, then such a prism is known as a regular prism.
2. Irregular Prism
The cross-section of an irregular prism is an irregular polygon.
Properties of Prism
1. A prism cannot have a circular cross-section or the shape of the base of a prism cannot be a circle.
2. A prism necessarily consists of all flat faces. Hence, a prism cannot have a curved surface.
3. The base and the top face of a prism are identical and are placed parallel to each other.
4. The cross-section of a prism remains the same throughout its length.
Examples of Prism
1. Carton Box
Carton boxes are generally manufactured in the shape of a cube or a cuboid. Both the cube and cuboid consist of two identical and parallel bases connected to each other with the help of four two-dimensional flat faces. Hence, they form a prominent example of prism-shaped objects used in our daily life.
2. Books and Notebooks
Books and notebooks are yet another example of the prism-shaped objects present around us. Typically, a book or a notebook consists of two congruent and parallel rectangle or square-shaped faces connected to each other with the help of four rectangular or square flat faces.
3. Rubik’s Cube
A Rubik’s cube is a prominent example of a square prism because it consists of six faces all of which are congruent and placed perpendicular to each other.
4. Ice Cubes
An ice cube is a block of frozen water that consists of six identical flat faces. The six square faces of an ice cube are aligned to each other at an angle of 90°.
Tents used for camping come in a variety of shapes and sizes. One of the most popular shapes in which a tent is manufactured is a triangular prism.
6. Chocolate Bar
Chocolate bars such as Toblerone form a classic example of the triangular prism-shaped objects present around us. One can easily identify the two triangular bases placed parallel to each other connected with the help of three rectangular faces.
The Pentagon, which is the headquarters of the U.S. Defense Department, is shaped like a pentagonal prism.
Clocks are manufactured in a variety of shapes and sizes such as rectangles, squares, pentagons, etc. Hence, one can easily observe the prism geometric shape in real life by observing the shape of a clock.
Nuts are the mechanical tools used in combination with bolts and washers to fasten two pieces of metals together. They are generally shaped like a hexagonal prism. One can easily identify the hexagonal shape of the bases of a nut placed parallel to each other connected with the help of six rectangles.
10. Unsharpened Pencil
If you observe the shape of an unsharpened pencil it consists of hexagonal bases that are connected to each other with the help of rectangular faces. Hence, an unsharpened pencil is one of the perfect examples of hexagonal prism-shaped objects used in our daily life.
11. Tissue Box
A tissue box is generally shaped like a cube or a cuboid. Both the cube and cuboid consists of two identical and parallel faces connected to each other with the help of four flat faces. Hence, they are a prime example of the rectangular and square prism-shaped objects used in our everyday life.
A dice typically consists of six square faces connected to each other at an angle of 90 degrees. Hence, the shape of a cubical dice is comparable to a square prism.
If you take out a triangular piece of cheese, you can easily observe that it is shaped like a triangular prism. The top and base of the cheese are shaped like a triangle and are connected to each other with the help of three rectangular flat faces.
14. Storage Boxes
Some of the storage boxes are shaped like a pentagonal prism. Two congruent pentagons are placed parallel to each other and are connected with the help of five two-dimensional rectangular faces.
If you look at the three-dimensional structure of a honeycomb, you can easily visualise the shape of a hexagonal prism. Hence, each section of a honeycomb forms a prime example of prism-shaped structures present around us.