Last updated: Jul 30, 2024

Cuboid Surface Area Calculator

Q: How do I find the length of a cuboid from it's surface area?

Let's assume that the surface area, height, and width are 288 , 4 , and 6 cm , respectively. Here is what we do: Use the surface area formula: s = 2(l×w + w×h + l×h) sq units . Make l the subject of the formula: l = (s/2 - wh)/(w+h) units . Substitute the values: l = (288/2 - 6 × 4)/(4+6) cm . Solve l = ( (144 - 24) / 10) cm . l = 120/10 cm . l = 12 cm .

Created by Adena Benn

Adena Benn

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Adena Benn is an Information Technology teacher with a degree in Computer Science. She has been teaching high schoolers since 1996 and loves everything computers. She loves problem-solving, so creating calculators to solve real-world problems is her idea of fun. She writes children's stories, is a seamstress, and is an avid reader. In her spare time, she travels and enjoys nature. See full profile

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Reviewed by Aleksandra Zając, MD

Aleksandra Zając

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A young Medical Doctor certified International Board of Lifestyle Medicine Diplomate. In one of the big Warsaw clinics, she's responsible for prophylaxis and medical education. Professionally interested in nutrition, exercise, and mental health. She wants never to stop learning and currently studies postgraduate psychodietetics. She likes to bake and play with her pets – one dog and four fancy mice. See full profile

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Table of contents

What does the word cuboid mean?How many vertices does a cuboid have?How to use this surface area of a cuboid calculator How to find the surface area of a cuboid Similar calculators FAQs

Are you at a loss as to how to calculate the surface area of a cuboid? Our cuboid surface area calculator will help you to sort out any questions or doubts you may have quickly and easily. Keep reading to learn:

The meaning of cuboid;
How many vertices a cuboid has;
How to use our surface area of a cuboid calculator;
The surface area of a cuboid formula; and
How to find the surface area of a cuboid manually.

What does the word cuboid mean?

A cuboid is a solid convex shape with each of its six faces shaped like a rectangle. It is also known as a rectangular prism. Some good real-world examples of cuboids are:

A book;
A mattress; and
A brick.

How many vertices does a cuboid have?

A cuboid has eight vertices. The vertices of a cuboid all form angles of 90 degrees.

How to use this surface area of a cuboid calculator

To use the surface area of a cuboid calculator, enter the following:

Length
Width; and
Height of the cuboid.

Our calculator will immediately return the total surface area of the solid.

Keep in mind you can use any units you wish - our tool will deal with it.

How to find the surface area of a cuboid

To find the surface area of the cuboid(s), you first need to:

Know the length (l), width (w), and height (h) of the shape.
Use the surface area of a cuboid formula:

\small s = 2(\text{l×w} + \text{w×h} + \text{l×h})\ \text{sq units}

Substitute the values for length, width and height - say 10, 7, and 8 cm, respectively. Then solve the equation

\small s = 2((10 × 7) + (7 × 8) + (10 × 8))\text{ cm}^2

Then solve the equation:

\small \begin{align*} s &= 2((10 × 7) + (7 × 8) + (10 × 8))\text{ cm}^2\\[.5em] &= 2((70) + (56) + (80))\text{ cm}^2\\[.5em] &= 2(206)\text{ cm}^2\\[.5em] &= 412\text{ cm}^2 \end{align*}

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FAQs

How do I find the length of a cuboid from it's surface area?

Let's assume that the surface area, height, and width are 288, 4, and 6 cm, respectively. Here is what we do:

Use the surface area formula:
s = 2(l×w + w×h + l×h) sq units.
Make l the subject of the formula:
l = (s/2 - wh)/(w+h) units.
Substitute the values:
l = (288/2 - 6 × 4)/(4+6) cm.
Solve
l = ( (144 - 24) / 10) cm.
l = 120/10 cm.
l = 12 cm.