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 .

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Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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Aleksandra Zając, MD

Aleksandra Zając

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Aleksandra (Ola) Zając, MD, is a medical doctor with a passion for lifestyle medicine. She wants to never stop learning while sharing what she already knows as a health educator and prophylaxis popularizer. She mainly concentrates on how human lifestyle impacts their health and disease. After hours, she likes weightlifting, foreign affairs podcasts, learning Korean, and dogs (with a special affection for her own pup Zoja). See full profile

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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.