Prism shape

Here you will learn about prism shapes, including how to classify and identify prism shapes.

Students will first learn about prism shapes as a part of geometry in 1st grade and continue to explore prism shapes in 6th grade.

What is a prism shape?

A prism shape is a 3D shape made up of flat faces, including two congruent polygonal bases and lateral sides connecting the bases. This page will cover right prisms, which have rectangular lateral faces.

For example,

Three main features of prisms are: faces, vertices and edges:

• Face – a closed, flat surface.
• Edge – connects two faces.
• Vertex (pl. vertices) – a point where three or more edges meet.

You can label the vertices (corners) of a prism to identify certain edges or faces. Below is an example of a triangular prism where the letters A-F represent the 6 vertices of the prism.

Using this labeling, you can identify lengths such as the length AB :

You can also identify faces such as the face ABC :

The number of faces, edges and vertices can vary depending on the prism. Let’s look at some examples:

Shape	Faces	Edges	Vertices
Triangular prism	5	9	6
Rectangular prism	6	12	8
Pentagonal prism	7	15	10
L-shaped prism (Hexagonal prism)	8	18	12

A prism is irregular if the base is not a regular polygon.

For example, the rectangular prism and L-shaped prism are irregular prisms because their bases are irregular polygons.

What is a prism shape?

Common Core State Standards

How does this relate to 1st grade math and 6th grade math?

• Grade 1: Geometry (1.G.A.2)
  Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

• Grade 6: Geometry (6.G.A.4)
  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

How to identify a prism shape

In order to identify a prism shape, you will:

1. Look for the characteristics of a prism.
2. State whether or not the shape is a prism.
3. If the shape is not a prism, explain what characteristics are different.

Volume of a prism examples

Example 1: identifying prisms

Is the shape below a prism?

1. Look for the characteristics of a prism.

The shape has 6 rectangular faces.

2State whether or not the shape is a prism.

This shape is a prism. Since the base is a rectangle, it is a rectangular prism.

Example 2: identifying prisms

Is the shape below a prism?

Look for the characteristics of a prism.

The shape has a circular base and no lateral faces.

Example 3: identifying prisms

Is the shape below a prism?

Look for the characteristics of a prism.

The shape has 7 faces.

Example 4: identifying prisms

Is the shape below a prism?

Look for the characteristics of a prism.

The shape has 4 faces.

Example 5: identifying prisms

Is the shape below a prism?

Example 6: identifying prisms

Is the shape below a prism?

Look for the characteristics of a prism.

The shape has 5 faces:

2 triangle bases and 3 rectangular lateral faces.

Teaching tips for prism shapes

• Worksheets are one way to have students practice types of prisms, but real-life exposure to these shapes is crucial. This can include working with 3D math manipulatives, creating the prisms and their nets and identifying prisms in the real world.

Easy mistakes to make

• Confusing edges and vertices
  Edges are the straight lines where two faces meet, while a vertex is a point where edges intersect.
  For example,
  
  

  

• Confusing 2D and 3D shapes
  When learning the names and properties of shapes, it can be easy to confuse them. With repeated exposure and conversations around these shapes, it becomes easier to remember them.

• Forgetting that bases are equal
  A prism has identical bases (or identical ends) that are connected by lateral faces. If a shape only has one base or the bases are not identical, the shape is not a prism.

• Thinking that oblique prisms are not prisms
  Though they are not typically introduced until later grades, oblique prisms fit the definition and are prisms. If younger students come across these in the real world or ask questions about these shapes, this gives an opportunity to discuss why they are prisms, but how they are different from right prisms.
  For example,
  The oblique rectangular prism below has two identical bases and parallelogram lateral faces.
  
  

  

Related prism shape lessons

• Rectangular prism
• Triangular prism

The next lessons are

• Types of data
• Average and range
• Representing data

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