Prism: A Complete Learning Guide

Introduction  

A prism is a three-dimensional geometric shape with two identical and parallel faces known as bases, and other faces that are parallelograms. Prisms are all around us, from buildings and books to packaging boxes and crystals. Understanding what a prism is, its types, and formulas like the volume of a prism is important in geometry and everyday situations.  

This guide will help you understand the meaning of a prism, explore different types like the right prism and oblique prism, and offer solved examples to reinforce your knowledge.  

 

Table of Contents  

• What is a Prism?
• Properties of a Prism
• Types of Prism
• Volume of Prism
• Surface Area of a Prism
• Difference Between Right Prism and Oblique Prism
• Applications of Prism in Real Life
• Common Misconceptions About Prisms
• Fun Facts About Prisms
• Solved Examples on Prisms
• Conclusion
• FAQs on Prism

 

What is a Prism?

A prism is a solid geometric shape with:  

•  Two congruent and parallel polygonal bases  

•  Flat faces (called lateral faces) that connect the corresponding sides of the bases  

•  The shape of the base determines the name of the prism (triangular prism, square prism, etc.)  

In simpler terms, you can picture a prism by extending a polygon straight up from its plane.  

 

Properties of a Prism

 A prism has two identical bases.  

•  The sides (lateral faces) are parallelograms.  

•  It has a uniform cross-section along its height.  

•  The number of faces, edges, and vertices depends on the base polygon.  

For example:  

A triangular prism has 5 faces, 9 edges, and 6 vertices.  

 

Types of Prism

There are mainly two classifications for types of prisms:  

Right Prism  

A right prism has lateral edges that are perpendicular to the base. This means its sides are rectangles, giving it an "upright" look.  

Features of a right prism:  

•  Lateral faces are rectangles.  

•  The angle between the base and sides is 90°.  

•  It is common in architecture and design.  

 

Oblique Prism  

An oblique prism has lateral edges that are not perpendicular to the bases, making it appear slanted.  

Features of an oblique prism:  

•  Lateral faces are parallelograms (not rectangles).  

•  The sides slant instead of being vertical.  

•  It is less commonly used in construction.  

 

Based on the Shape of the Base  

The name of a prism changes depending on the polygon used for the base. Some examples include: 

•  Triangular prism  

•  Rectangular prism  

•  Pentagonal prism  

•  Hexagonal prism  

•  Octagonal prism  

Each follows the same rules of a prism, differing only in the shape of the base.  

 

Volume of Prism

The volume of a prism is found using the formula:  

Volume of Prism = Base Area × Height  

Where:  

 Base Area = area of the polygon at the base  

 Height = distance between the two bases (perpendicular height)  

Examples:  

Volume of a triangular prism = (½ × base × height of triangle) × height of prism  

Volume of a rectangular prism = length × width × height  

 

This formula applies to all types of prisms, whether right or oblique (if the perpendicular height is used).  

 

Surface Area of a Prism

Surface area includes the area of all faces (two bases plus lateral sides).  

Surface Area = 2 × Base Area + Perimeter of Base × Height  

This helps calculate how much material is needed to cover the prism.  

 

Difference Between Right Prism and Oblique Prism

 

 

This table shows the structural differences between a right prism and an oblique prism.  

 

Applications of Prism in Real Life

•  Optics: Glass prisms split white light into different colours.  

•  Architecture: Many buildings use rectangular prism shapes.  

•  Engineering: Bridges and supports often utilise prism structures for stability.  

•  Packaging: Many boxes are prism-shaped (rectangular prisms).  

•  Crystals: Natural minerals often form prism-like shapes.  

You can find some form of a prism everywhere!  

 

Common Misconceptions About Prisms

•  Only rectangular prisms are prisms.  

   False. Any polygonal base (triangle, pentagon, etc.) can form a prism.  

•  All prisms have right angles.  

   Not true. Oblique prisms have slanted angles with the base.  

• Only regular polygons can form prisms.  

   Any polygon (regular or irregular) can serve as the base of a prism.  

• The height is always the side length.  

   No. The height is the perpendicular distance between the bases.  

• You can't calculate volume if it's oblique.  

   You can, as long as you use the perpendicular height in the volume of a prism formula.  

 

Fun Facts About Prisms

•  Isaac Newton used a glass prism to show that white light is made of seven colours.  

•  A triangular prism can refract light twice and flip an image!  

•  Prism-shaped packaging is easier to stack and transport.  

•  Prisms are used in binoculars and periscopes to reflect light.  

•  Crystals like quartz naturally grow in the shape of hexagonal prisms.  

These facts highlight how fascinating and useful prisms are beyond geometry class!  

 

Solved Examples on Prisms

Example 1: 

Find the volume of a rectangular prism with length = 5 cm, width = 3 cm, and height = 4 cm.  

Ans: Volume = 5 × 3 × 4 = 60 cm³  

 

Example 2:

 A triangular prism has a base triangle with base = 6 cm and height = 4 cm. The prism’s height is 10 cm.  

Ans: Volume = (½ × 6 × 4) × 10 = 12 × 10 = 120 cm³  

 

Example 3: 

What is the surface area of a rectangular prism with l = 4 cm, w = 2 cm, h = 3 cm?  

Ans: SA = 2(lw + lh + wh) = 2(8 + 12 + 6) = 2 × 26 = 52 cm²  

 

Example 4: 

Identify whether a slanted box is a right prism or an oblique prism.  

Ans: Since it is slanted, it is an oblique prism.  

 

Example 5:

 A pentagonal prism has a base area of 30 cm² and a height of 8 cm. Find the volume.  

Ans: Volume = 30 × 8 = 240 cm³  

These problems reinforce your understanding of the volume of prisms, types, and real-world problem-solving.  

 

Conclusion

A prism is an important 3D shape in geometry with many real-world uses. By learning about the types of prisms, including right and oblique prisms, understanding how to find the volume, and exploring their properties, students can greatly improve their spatial and geometric skills.  

From classrooms to crystal labs, and buildings to bookshelves, prisms are everywhere. With this complete guide, you now have the tools to recognise, classify, and solve problems involving prisms confidently!

 

Frequently Asked Questions on Prism

1. What is called a prism?

Ans: A prism is a 3D solid object with two identical polygonal bases and flat rectangular faces joining the corresponding sides.

 

2. What is the prism formula?

Ans: The volume of a prism = Base Area × Height. Surface Area = 2 × Base Area + Perimeter of Base × Height.

 

3. How to calculate a prism?

Ans: To calculate the volume, multiply the area of the base by the height. For surface area, calculate the area of all faces and add them.

 

4. What is the law of a prism?

Ans: In optics, the prism law relates the deviation angle of light through a prism to its angle and refractive index:
δ = (n - 1) × A,
Where δ is the deviation, n is the refractive index, and A is the prism angle.

 

Learn all about prisms and formulas at Orchids The International.