Rectangular prism

Here you will learn about rectangular prisms, including how to classify and identify rectangular prisms.

Students will first learn about rectangular prisms as a part of geometry in 1 st grade.

Every week, we teach lessons on rectangular prisms to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with 6 rectangular faces where all the faces (one at the top, one at the bottom and four lateral faces) meet at right angles. They are also known as cuboids.

Cubes are a special type of rectangular prism where the length, width and height are all equal.

Examples of a rectangular prism:

Real life examples of rectangular prisms include shoe boxes, books and even the bricks on your house.

Properties of a rectangular prism

The properties of a rectangular prism include faces, edges, vertices (corners), length, width and height.

Faces

A face of a 3D shape is a flat surface.

Rectangular prisms have a total of \bf{6} faces – all of which are rectangular (or square). As a result of having rectangular bases, the other faces are also rectangles.

Edges

An edge of a 3D shape is a straight line between two faces.

Rectangular prisms have \bf{12} edges:

Vertices

A vertex is a point where two or more edges meet.

Rectangular prisms have \bf{8} vertices:

Length, width and height

A rectangular prism has three dimensions: length, width, and height.

The length refers to the measurement from one end of the rectangular prism to the other, the width is the measurement from side to side, and the height of the rectangular prism is the measurement from top to bottom.

Labeling a rectangular prism

You can label the vertices (corners) of a rectangular prism to help us identify certain edges or faces.

For example,

Using this labeling you can identify lengths, for example, the length AB :

You can also identify faces, for example, the face ABCD :

What is a rectangular prism?

Common Core State Standards

How does this relate to 1 st 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.

How to identify a rectangular prism

In order to identify a rectangular prism, you will:

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

Rectangular prism examples

Example 1: rectangular prism example

Look at the image below and determine if it is a rectangular prism or not.

1. Look for the characteristics of a rectangular prism.

The shape has 4 triangular and 1 rectangular face, not 6 rectangular faces.

2State whether or not the shape is a rectangular prism.

This shape is not a rectangular prism, this shape is a pyramid.

3If the shape is not a rectangular prism, explain what characteristics are different.

This shape is not a rectangular prism because it has 4 triangular and 1 rectangular face.

Example 2: identify rectangular prisms

Look at the shape below and determine if it is a rectangular prism or not.

Look for the characteristics of a rectangular prism.

The shape has 6 square faces.

The shape has 8 vertices, or corners.

The shape has 12 edges.

Are the side lengths different from each other?

No, all the sides are the same length.

Example 3: real-world example

Look at the image below and determine if it is a rectangular prism or not.

Look for and identify the characteristics of a rectangular prism.

The fish tank has 6 rectangular faces.

The fish tank has 8 vertices, or corners.

The fish tank has 12 edges.

Are the side lengths different from each other?

Yes, you can see that the sides on top and bottom are longer than the sides on the left and right.

How to identify a rectangular prism in a 3D composite shape

In order to identify rectangular prisms in a composite shape, you will:

1. Count the number of shapes that make up the composite shape.
2. Identify and count the number of rectangular prisms within the shape.
3. State the number of rectangular prisms within the composite shape.

Example 4: identify rectangular prisms within a 3D composite shape

Look at the composite shape and identify all rectangular prisms.

Identify and count the number of rectangular prisms within the shape.

Each of these shapes has 6 regular faces that meet at right angles.

Example 5: identify rectangular prisms within a 3D composite shape

Look at the composite shape and identify all rectangular prisms.

Identify and count the number of rectangular prisms within the shape.

Each of these shapes has 6 regular faces that meet at right angles.

Example 6: identify rectangular prisms within a 3D composite shape

Look at the composite shape and identify all rectangular prisms.

Identify and count the number of rectangular prisms within the shape.

Each of these shapes has 6 regular faces that meet at right angles.

Teaching tips for rectangular prisms

• Allow students the opportunity to explore and manipulate real-life examples of a rectangular prism. Some real-life examples of rectangular prisms are shoeboxes, books, refrigerators, and televisions. These objects have a box-like shape with rectangular sides.

• Provide students with physical rectangular prisms or building blocks to explore and manipulate. This hands-on approach helps them visualize and understand the properties and dimensions of rectangular prisms.

• With upper elementary students, in lue of working with rectangular prisms on worksheets, allow students to measure and compare the length, width, and height of rectangular prisms using rulers or measuring tapes. This helps reinforce the concept of dimensions and encourages critical thinking.

• Provide students with real-world practice problems or puzzles that involve rectangular prisms. For example, ask middle schoolers to calculate the volume or surface area of a rectangular prism or find the dimensions of an object given its properties.

• With students of all ages, draw connections between rectangular prisms and other geometric shapes, such as squares, rectangles, and cubes. Discuss similarities and differences in their properties to reinforce understanding.

Easy mistakes to make

• Assuming cubes are not rectangular prisms
  Some definitions of rectangular prisms note that the sides are different lengths, meaning a cube could not be a rectangular prism. However, cubes are a special kind of rectangular prism, and should be considered one.

• Confusing edges and vertices
  An edge is a line segment where two faces meet, while a vertex is a point where edges intersect.

• Confusing rectangles and rectangular prisms
  Rectangles are 2D (they are made up of a length and width and are flat), and rectangular prisms are 3D (they are made up of rectangular faces and are not flat).

Related prism shape lessons

• Prism shape
• Triangular prism

The next lessons are

• Types of data
• Average and range
• Representing data

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