Today, we're going on an exciting journey to discover the world of 3D shapes, focusing on a super cool shape called "Prism." Ever wondered what a prism is and how it fits into math? You're in luck! We'll explain everything in a way that's easy to understand, breaking down complex ideas into simple language.

Prism definition - Math 2023

Imagine a magic shape that can split light into a beautiful rainbow of colours! That's a prism! Prisms are like special glasses for light. They are 3D shapes with two flat sides (like faces) that are the same shape, and they're connected by cool-looking sides. You can think of them as sparkly gems, making everything more colourful!

In simple math language, a prism is a three-dimensional geometric shape characterised by two parallel and congruent polygonal bases, connected by a set of parallelogram faces. Prisms are a fascinating topic in geometry and are widely studied due to their numerous applications in various fields, such as architecture, engineering, and physics.

Differentiation between Prism and Pyramid

Feature	Prism	Pyramid
Shape	A prism has two identical, parallel bases that are polygons (usually rectangles or triangles), connected by rectangular or parallelogram sides.	A pyramid has one polygonal base (like a triangle, square, or pentagon) and triangular sides that meet at a single point called the apex.
Number of Bases	Prisms have two bases.	Pyramids have only one base.
Vertices and Edges	Prisms have the same number of vertices and edges on both bases.	Pyramids have fewer vertices and edges on the base compared to the apex.
Faces	Prisms have three or more rectangular faces (including the bases).	Pyramids have triangular faces (including the base) that meet at the apex.
Examples	Examples of prisms include a rectangular prism (like a book) or a triangular prism (like a tent).	Examples of pyramids include a square pyramid (like a pyramid in Egypt) or a triangular pyramid (like a pyramid-shaped cake).

Colourful Light Show!

Do you know why rainbows look so magical? It's all because of prisms! When light passes through a prism, it gets all playful and bends, just like when you slide down a slide at the playground! This bending of light makes the colours separate and form a pretty rainbow.

Prism

Prism Science - Cross Section of a Prism

Imagine you have a colourful prism, and you take a special knife and cut it right along its middle, like cutting a yummy cake. The shape you get from that cut is called the "Cross Section."

Now, here's the exciting part! If you cut the prism that's perfectly parallel to the base (the bottom part), guess what? The shape of the cross-section will be just like the base! Wow!

For Example,

Let’s say you have a square pyramid, like a pyramid with a square base. If you cut it with a plane that's flat and parallel to the square base, ta-da! The cross-section shape will also be a square!

Isn't that awesome? It's like finding a secret hidden shape inside the prism. Remember, the cross-section will always look like the base when you cut the prism the right way!

Characteristics of Prisms

Prisms are like magical 3D shapes with exciting features! Let's learn about their special characteristics together:

• Bases: Prisms have two bases that are flat and look like cool shapes, such as triangles, rectangles, or other polygons. Imagine two colourful floors at the top and bottom of a prism!

• Lateral Faces: The sides of a prism are called lateral faces. They look like colourful walls connecting the bases. These walls are super special because they are all flat and have the same shape and size.

• Edges: Look at the edges of a prism! They are like colourful lines that connect the corners of the bases. Imagine drawing lines to connect the corners of two shapes – that's how the edges of a prism look!

• Vertices: The corners of the bases are called vertices. Guess what? A prism has two sets of vertices – one set for each base. Count all the corners on the top and bottom, and you'll find all the vertices of the prism!

Types of Prisms

There are various types of prisms based on the shape of their bases. Some common examples include:

Triangular Prism:

A triangular prism has two triangular bases connected by three rectangular lateral faces. The lateral faces are parallelograms. Triangular prisms are commonly encountered in day-to-day objects, such as triangular roof structures or packaging boxes with a triangular cross-section.

Rectangular Prism (Cuboid):

A rectangular prism, also known as a cuboid, has two rectangular bases connected by four rectangular lateral faces. This is one of the most familiar prisms as it resembles a standard box or a rectangular room in a building.

Pentagonal Prism:

A pentagonal prism has two pentagonal bases connected by five parallelogram-shaped lateral faces. Pentagonal prisms are less common in everyday objects, but they are still essential geometric shapes, especially in certain architectural designs.

Hexagonal Prism:

A hexagonal prism has two hexagonal bases connected by six parallelogram lateral faces. These types of prisms are also encountered in specific architectural and engineering applications.

Octagonal Prism:

An octagonal prism has two octagonal bases connected by eight parallelogram lateral faces. Octagonal prisms are less frequently seen in everyday objects but are still significant in geometry and design.

Tri-Rectangular Prism (Right-angled Triangular Prism):

A tri rectangular prism has two triangular bases, one of which is a right-angled triangle, and the other two lateral faces are rectangles. This type of prism combines aspects of triangular and rectangular prisms.

Trapezoidal Prism:

A trapezoidal prism has two trapezoidal bases connected by four lateral faces that are parallelograms. Trapezoidal prisms are used in various architectural and engineering structures.

Rhombic Prism:

A rhombic prism has two rhombus-shaped bases connected by four parallelogram lateral faces. This type of prism is less common but still important in certain mathematical concepts.

Volume of a Prism

One of the essential properties of a prism is its volume, which represents the amount of space the prism occupies. To calculate the volume of a prism, you can use the formula:

💡

Volume = Base Area × Height

The base area refers to the area of one of the bases (as they are congruent), and the height is the perpendicular distance between the two bases.

For example, the volume of a rectangular prism can be found by multiplying the length and width of the base (l × w) by the height (h):

Volume = l × w × h

Applications of Prisms

Prisms are like special tools that help us do incredible things. They have super cool applications in different areas:

• Architecture Magic: Architects use prisms to design unique and awesome buildings! They can create buildings with interesting shapes and sizes, making our cities look fantastic!
• Engineering Wonders: Engineers love prisms too! They use them to build strong structures like bridges, roofs, and even big tanks. Prisms help make these structures sturdy and safe for everyone.
• Light Tricks: Prisms are like magicians with light! They can split light into beautiful colours, like a colourful rainbow. That's why we have cool things like cameras and spectacles to see better.
• Secret Codes: In science labs, prisms help scientists study and understand light better. They help unlock secrets and discover new things about our world!

Mathematics is an adventure waiting to be explored, and understanding prisms is just one step on this exciting journey. So, whether you're an aspiring mathematician, a curious learner, or someone looking to refresh their knowledge, remember that with a little imagination and a touch of curiosity, mathematics can become a fascinating and enjoyable exploration! Happy learning!