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: = (288/2 - 6 × 4)/(4+6) cm . Solve =( (144 - 24) / 10) cm . =120/10 cm . =12 cm . Read more

Created by Adena Benn

Reviewed by Aleksandra Zając, MD

Last updated: Jun 05, 2023

Table of contents:

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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FAQ

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:
= (288/2 - 6 × 4)/(4+6) cm.
Solve
=( (144 - 24) / 10) cm.
=120/10 cm.
=12 cm.

Adena Benn

image of a rectangular prism, with length, height, width and diagonal marked

Length (l)

Width (w)

Height (h)

Surface area (s)

Diagonal (d)

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