A Detailed Analysis of Prisms

Prism is a solid shape with two parallel and identical polygons on two of its faces and parallelograms on the rest of the faces linking them. We’ll go through numerous prism formulas, different types of prisms, and more in this section. The major distinction between right and oblique prisms is that a right prism’s lateral sides are rectangles rather than parallelograms.

History

The Elements, one of Euclid’s mathematical treatises, was the first to mention prism. A prism is defined as “a solid figure encompassed by two opposed, equal, and parallel planes, while the remainder is parallelograms” in the book. 

Applications of prism

• Beam-splitter cubes can be made with right-angled prisms.
• Right-angled prisms can rotate images by 90° or 180 °. The angle and direction inversion is determined by the prism’s orientation.
• In binoculars and telescopes, a prism system known as the porro system is used. This is utilised because a picture can be rotated 180 degrees while maintaining its orientation (right-left handed).
• Architectural hexagonal prisms are employed. In Sweden, triangular prism constructions are used to prevent snow from piling up on rooftops.

Types of prism

The following are the types of prisms.

1. Rectangular prism

A cuboid is a rectangular prism made up of two congruent rectangular bases that are 90 degrees apart. With the help of four more rectangles, the edges of the rectangular bases are joined to produce a three-dimensional geometric shape with all flat faces.

2. Square prism

A square prism’s bases, as the name suggests, are square. These bases are parallel to each other and are congruent. When four two-dimensional square faces are utilised to connect the two parallel and congruent bases of a square prism with similar dimensions, a cube-geometric structure is generated.

3. Triangular prism

A two-dimensional triangle is one of the popular types of prisms. These parallel triangular bases are connected by three similar rectangular faces. Because it has five faces, a triangular prism is called a pentahedron.

4. Prism with a pentagon

A five-sided polygon or a pentagon is the shape of the base of a pentagonal prism. It is made up of five rectangular faces that link the prism’s base.

5. Hexagonal prism

A hexagonal prism is a three-dimensional geometric form made up of two congruent hexagonal bases positioned parallel to each other and joined by six rectangular sides.

Classification on the basis of cross-section

Let’s understand the classification based on the cross-section of prims. 

1. Regular prism

A prism is called a regular prism if the cross-section of the prism is shaped like a regular polygon.

2. Irregular prism

An irregular prism’s cross-section is an irregular polygon.

Real-life examples of prism

1. Corrugated box

In general, corrugated boxes are made in the shape of a cube or a cuboid. Both the cube and the cuboid are made up of two identical and parallel bases that are joined by four two-dimensional flat sides. As a result, they are a common example of prism-shaped items in our daily lives.

2. Books and notebooks

Books and notebooks are other examples of prism-shaped things seen in our environment. Two congruent and parallel rectangles are joined by four rectangles. 

3. Rubik’s cube

Because it has six congruent faces that are all perpendicular to each other, a Rubik’s cube is a well-known example of a square prism.

4. Ice cubes

A block of frozen water with six equal flat faces is known as an ice cube. The six square faces of an ice cube are at a 90° angle to each other.

5. Tents

Camping tents come in a range of designs and sizes. A triangular prism is one of the most prevalent tent shapes.

6. Chocolate bar

Toblerone chocolate bars are a great example of the triangular prism-shaped things that may be found all around us. The two triangular bases that are parallel to one other and joined by three rectangular faces are immediately identifiable.

7. Buildings

The Pentagon, which houses the US Defense Department’s headquarters, is shaped like a pentagonal prism.

8. Clocks

They come in a range of forms and sizes, including rectangles, squares, and pentagons. As a result, the prism geometric shape can be easily observed in real life by observing the shape of a clock.

9. Nuts 

Nuts are mechanical fastening tools that are used in conjunction with bolts and washers to join two metal pieces together. They usually have a hexagonal prism form. The hexagonal shape of a nut’s base, which is parallel to each other and joined by six rectangles, is immediately identifiable.

Conclusion

This should give you a good understanding of what a prism is and what the types of prisms are. To summarise, it is a polygon belonging to the polyhedron family with congruent polygons at the base and top. A prism’s other faces are its lateral faces. It denotes the absence of a curved face on a prism. The cross-section of a prism is the same all the way around. The cross-sections of the prisms are used to name them.