What is a Square Prism?

Brigette Banaszak, Joseph Vigil
  • Author
    Brigette Banaszak

    Brigette has a BS in Elementary Education and an MS in Gifted and Talented Education, both from the University of Wisconsin. She has taught math in both elementary and middle school, and is certified to teach grades K-8.

  • Instructor
    Joseph Vigil

    Joseph has a master's degree in literature as well as alternative teaching and ESL educator certifications. He has worked with middle school, high school, and college students in writing and language arts.

Learn about square prisms. Identify what a square prism is, discover how to find the volume and area of a square prism, and examine types of square-based prisms. Updated: 12/19/2021

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What Is a Square Prism?

What is a prism? A prism is a three-dimensional solid with two congruent, parallel bases joined together by flat sides. A prism is named by the shape of its parallel bases, so a square prism is a prism with two congruent, parallel, square bases. A rectangular prism, on the other hand, has two congruent, parallel, rectangular bases. In the example, the square prism has two square bases (in red) and four rectangular sides (in yellow and blue). All square prisms are not cubes, although all cubes are square prisms.

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Square prism

Square prism

Properties of a Square Prism

What are the properties of a square prism? A square prism has:

  • 6 faces: A face is a flat side on a three-dimensional solid shape. Opposite faces are congruent and parallel.
  • 12 edges: An edge is the line segment where two faces meet.
  • 8 vertices: The singular form of vertices is vertex. A vertex is a point, somewhat like a corner, where three or more edges meet.
  • 1 set of congruent, parallel, square bases: A square prism can have more than two square bases, but there must be at least two.

Labeled square prism

Labeled square prism

The diagram shows several three-dimensional solids with edges and vertices labeled. There are two prisms, and one of them is a square prism. The 12 edges and 8 vertices on the square prism are marked.

Labeled edges and vertices

Labeled edges and vertices

The other two solids are a triangular prism, which has triangle bases, and a square pyramid. Notice how the pyramid has only one square base.

Oblique vs. Right Square Prisms

There are two kinds of square prisms:

  • A right square prism has sides that are perpendicular to its bases. This means the two bases will line up, one directly above the other.
  • In an oblique square prism, the sides are not perpendicular to the prism's bases. Although the two bases will be congruent and parallel, one is not directly over the other.

Right and oblique prisms

Right and oblique prisms

The prisms shown in the diagram are hexagonal, not square, prisms, but they demonstrate the difference between a right prism and an oblique prism. The yellow prism on the left is a square prism, and the blue prism on the right is an oblique prism.

Square Prism Examples

What are some real-world examples of square prisms?

A cube, such as these puzzle cubes, is an example of a square prism because it is a three-dimensional shape with at least two square sides.

Puzzles cubes

Puzzle cubes

This number cube is also a square prism.

Square prism number cube

Square prism number cube

This box of tissue is another example of a cube, which is a square prism.

Tissue box

Tissue box

These school lockers are square prisms because the bases of the lockers are squares.

School lockers

School lockers

A stack of several square crackers, one on top of the other, would make a square prism.

Square crackers

Square crackers

A closed pizza box is a square prism.

Pizza box

Pizza box

In fact, any kind of box might be a square prism, whether used for moving, holding jewelry, or storing compact discs.

Boxes

Boxes

Even a building can be a square prism, as long as the ground floor base is shaped like a square.

Building

Building

Net of a Square-Based Prism

A square prism is a three-dimensional shape. Three-dimensional shapes can be constructed from flat, two-dimensional nets.

The net of a right square-based prism will consist of at least two squares. The other sides may be either square or rectangles.

Net of right square prism

Net of right square prism

The net of an oblique square-based prism will also consist of two squares, The other sides will be rhombuses or parallelograms.

Oblique prism net

Oblique prism net

Square Prism Formulas

What is the area of a square prism? Since a square prism is a three-dimensional shape, it has a surface area rather than an area. The surface area of a square pyramid is the area of the outside of the prism. To find the surface area of a prism, find the sum of the areas of the prism's faces.

Look at the nets of the square prisms. Each net consists of two square bases, and either a large rectangle composed of four smaller rectangles or a large parallelogram composed of four smaller parallelograms. The large rectangle or parallelogram composed of four smaller shapes represents the sides of the prism. To find the surface area, find the area of the two square bases, and add to that total the area of the large shape composed of the lateral sides. That larger shape has a width that is equal to the perimeter of the base of the square prism, and a length that is equal to the height of the prism. So, the formula for the surface area of a square prism is:

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Frequently Asked Questions

What's the difference between a square prism and a rectangular prism?

A square prism has two congruent, parallel square bases, while a rectangular prism has two congruent, parallel rectangle bases. Every square prism is also a rectangular prism, since all squares are also rectangles.

How do you find the surface volume of a square prism?

To find the surface area of a square prism, find the sum of the areas of the prism's faces. The formula is Surface area = 2B + Ph, where B = the area of a square base, P = the perimeter of the square base, and h = the height of the prism.

Is a cube a prism?

A cube is an example of a square prism. A cube has two congruent, parallel, square bases, which makes it a square prism.

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