Rectangular Prism: Definition and Example Tasks

By: Tasha Kolesnikova

5 min

5

10.04.2022

Geometry students frequently receive assignments that require them to compute the volume, cross-sectional area, or surface area of a rectangular prism. At first glance, this might seem tricky, but it really comes down to a simple formula. In this guide, we’ll explain the concept of rectangular prisms, break down the volume formula, and give real examples.

What Is a Rectangular Prism?

Rectangular prism

Rectangular prism, also known simply as a "prism" or "rectangular cuboid," — is a three-dimensional geometric shape characterized by six rectangular faces, twelve straight edges, and eight vertices (corners).

A rectangular prism must:

• Be a 3-dimensional shape (has height, width, and depth)
• Have polygonal, parallel faces
• Be a hexahedron
• Have parallelogram-shaped sides: this is important and distinguishes a rectangular prism from a triangular prism
• Have 12 edges and 8 vertices

Types of Rectangular Prisms

There are 2 types of rectangular prisms: cuboid and oblique.

• Cuboid: All of a cuboid’s angles are right angles, and its opposite faces are equal and parallel. This three-dimensional object can also be called a right rectangular prism. Note: cubes are cuboids, but not all cuboids are cubes. Some real-life examples of right rectangular prisms/cuboids include aquariums and refrigerators.

• Oblique rectangular prism: This does not have bases that are perpendicular to its lateral faces.

How to Calculate the Volume of a Rectangular Prism

Finding the volume of a rectangular prism is an incredibly simple task! It’s much easier and quicker than, for instance, finding its total surface area. All you have to do is multiply its 3 dimensions. The formula is as follows:

Volume of rectangular prism = length x width x height

Be sure to express your answer in cubic units; otherwise, it might be marked wrong.

Now, here’s a special case: what if you only know the area of the base and the height of the prism? Guess what! You can also solve the volume problem with this formula:

Volume = area of the base x height

Why does this work? Well, the faces are parallelograms, and a parallelogram’s area = length x width. Thus, if your worksheet provides the rectangular prism’s area of base and height, you automatically know its length and width as well.

Rectangular Prism Calculator

Example #1

Now that you know the formula for finding the volume of a rectangular prism, let’s work through a basic example:

We can see that the height of this prism is 4 cm, the width is 3 cm, and the length is 6 cm. Now, just plug those numbers into the formula! Step-by-step, here’s what to do:

Volume of = length x width x height

Volume of = 6 cm x 3 cm x 4 cm

Volume of = 72 cm3

Remember to express your answer in cubic units (that little three in front of cm). Because the volume of any object is measured in three dimensions, it will always be expressed this way.

Example #2

Let’s try another example! Some worksheets show rectangular prisms as their actual cubic units, as seen in the picture below:

So, first count the cubes in the length: 4. Next, width: 2. Lastly, height: 2.

Multiply them!

Volume = 4 cubic units x 2 cubic units x 2 cubic units

Volume = 16 cubic units

Note: When we are measuring like this, there’s no need to put the little 3. Saying 16 cubic units3 is equivalent to saying 4,096 cubic units, which is definitely the wrong answer!

Summary

As you can see, solving the volume of a rectangular prism is extremely simple. It doesn’t matter if the prism is oblique or cuboid: all you need to do is remember the formula V = l x w x h, and just plug the numbers in. Finding the surface area of a rectangular prism would be a little more complex, but barely – we can cover that in another guide.

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I studied sociology and marketing at Europa-Universität Viadrina (Germany) and Universidade da Beira Interior (Portugal). When I was a sophomore, back in 2018, I decided to put what I've learned into practice, so I got my first job in digital marketing. I currently work in the content marketing department at Studybay, building strong, effective, and respectful communication between the platform and our clients.

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• I didn't realize there were so many types of rectangular prisms beyond just basic boxes. Learning examples like cuboids, cubes, and parallelepiped was fascinating! Seeing models of the subtle differences between them really hammers the unique shapes home. This is such an informative article on these 3D forms.👌

Pearl

02.26.2024

• You explain the conceptual parts well too - like the difference between surface area and volume. Putting the math in context helps develop a deeper understanding.

Caroline

03.01.2024

• The embedded calculator that figures out the surface area and volume for you is awesome! It's so quick and easy to get the math done. Much easier than doing it all manually.

Ava-Rose

03.14.2024

• I appreciate you covering how to calculate the surface area and volume for rectangular prisms. Walking through examples of finding both is super helpful for getting the formulas down.

Chelsea

02.06.2024

• Great explanations on the characteristics! The illustrations really help visualize and identify these 3D shapes clearly.

Isobelle Dunn

02.04.2024

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