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How to Measure the Surface Area of a Cuboid

We recently wrote about how to measure the volume of a cuboid. Today, we’ll tackle how to measure the surface area of a cuboid.

What is a cuboid?


A cuboid, also called a rectangular prism, is a solid three-dimensional box that has six faces that are all rectangles. Here’s an example of a cuboid:
 
Cuboid


What is surface area?


The surface area of a cuboid is a measure of the total area that the surface of that box, basically the area of all six sides.

How do we measure the surface area of the cuboid?


We now know that a cuboid has six rectangular faces. Also, if you look carefully, the two surfacea areas that oppose each other are the same size, or take up the same surface area.


The width and length sides are the same surface area:
width and length of cuboid 


The length and height sides are the same surface area:

length and height of cuboid
 
The height and width sides are the same surface area:

height and width of cuboid
 
We also mentioned that the surface area of the cuboid is the area of all six sides.


With that in mind, we have:


two sides of the surface area of width and length

two sides the surface area of length and height

two sides the surface area of the height and width

Adding all six sides together, therefore, means adding:

2 x width x length

With

2 x length x height

With

2 x height x width


The formular for calculating the surface area is:


Area = 2 x width x length + 2 x length x height + 2 x height x width


This can be shortened to:


Formula for surface area of cuboid 



Let’s use an example.

 

surface area of cuboid example
 
Area = 60 + 100 + 30
The answer is: surface area = 190 in
The surface area of this cuboid is 190 inches.