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Introduction

QUICK LINKS


Introduction

Surface Area of Cubes and Rectangular Prisms

INTRO
The surface area of a 3D shape is equal to the sum of the areas of all the faces (sides) of that shape. A helpful way to think about it is:
surface area = sum of face areas
We can also think about surface area in terms of gifts! The surface area is like the minimum amount of wrapping paper we need to prep a gift for its surprise reveal. 🤩If we were to unwrap a gift, the amount of wrapping would be equal to the surface area of the object it was covering.

Pick a gift shape to unwrap:

When we “unwrap” a 3D shape, we get what we call a net. A surface area net shows us the different 2D shapes that make up the faces of the 3D shape.
We can then find the area of each face and then add them all together to find the total surface area.
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the surface area of cubes and rectangular prisms and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

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CALCULATOR

Surface Area of Cubes & Rectangular Prisms Calculator

What is your shape?

Step 1. Unwrap the cube.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the cube.

Sides with the same color mark are the same size 🎉.
ShapeArea
1
(Square)
2
(Square)
3
(Square)
4
(Square)
5
(Square)
6
(Square)

Step 3. Add up the areas of the shapes that make up the cube.

The surface area of this cube is .
KEY STEPS

How to Find Surface Area of Cubes and Rectangular Prisms

Shape

Step 1. Unwrap the cube.

Step 2. Calculate the area of each part of the net that makes up the cube.

Squares 1 - 6

Step 3. Add up the areas of the shapes that make up the cube.

LESSON
Surface Area of Cubes

Surface Area of Cubes

The surface area of a cube is equal to the sum of the areas of all the faces (sides) of the cube. If we unwrap a cube, we can see that the net is made up of identical squares.So, we only need to find the area of one of the squares (), and add it times (or multiply it by ) to get the total surface area!Let's unwrap some more cubes to find their surface area!

EXAMPLE 1

Let's start here - find the surface area of this cube:
What is your shape?

Step 1. Unwrap the cube.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the cube.

Now, we'll find the area of each shape in the net. Notice that some shapes have the same area:
Sides with the same color mark are the same size 🎉.
ShapeArea
1
(Square)
2
(Square)
3
(Square)
4
(Square)
5
(Square)
6
(Square)

Step 3. Add up the areas of the shapes that make up the cube.

The surface area of this cube is .

EXAMPLE 2

Nice work! Try another one:
What is your shape?

Step 1. Unwrap the cube.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the cube.

Now, we'll find the area of each shape in the net. Notice that some shapes have the same area:
Sides with the same color mark are the same size 🎉.
ShapeArea
1
(Square)
2
(Square)
3
(Square)
4
(Square)
5
(Square)
6
(Square)

Step 3. Add up the areas of the shapes that make up the cube.

The surface area of this cube is .
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're dealing with rectangular prisms.
PRACTICE
Surface Area of Cubes

Practice: Surface Area of Cubes

Question 1 of 5: Find the surface area of this cube:

Step 1. Unwrap the cube.

Step 2. Calculate the area of each shape in the net.

Since all the shapes in the net of a cube are identical squares, we only need to find the area of one of the squares.
ShapeArea
1
(Square)

Step 3. Add up the area of all the shapes that make up the cube.

Awesome job! The surface area of the cube is .

LESSON
Surface Area of Rectangular Prisms

Surface Area of Rectangular Prisms

The surface area of a rectangular prism is equal to the sum of the areas of all the faces (sides) of the rectangular prism.
If we unwrap a rectangular prism, we can see that the net is made up of pairs of identical rectangles.
So, we only need to find the area of one rectangle from each pair. Then we double each of the three rectangle areas and add them together!
Let’s unwrap some more rectangular prisms and find their total surface areas!

EXAMPLE 1

Let's start here - find the surface area of this rectangular prism:
What is your shape?

Step 1. Unwrap the rectangular prism.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the rectangular prism.

Now, we'll find the area of each shape in the net. Notice that some shapes have the same area:
Sides with the same color mark are the same size 🎉.
ShapeArea
1
(Rectangle)
2
(Rectangle)
3
(Rectangle)
4
(Rectangle)
5
(Rectangle)
6
(Rectangle)

Step 3. Add up the areas of the shapes that make up the rectangular prism.

The surface area of this rectangular prism is .

EXAMPLE 2

Amazing! Try this one now:
What is your shape?

Step 1. Unwrap the rectangular prism.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the rectangular prism.

Now, we'll find the area of each shape in the net. Notice that some shapes have the same area:
Sides with the same color mark are the same size 🎉.
ShapeArea
1
(Rectangle)
2
(Rectangle)
3
(Rectangle)
4
(Rectangle)
5
(Rectangle)
6
(Rectangle)

Step 3. Add up the areas of the shapes that make up the rectangular prism.

The surface area of this rectangular prism is .
Awesome! If you’d like to practice additional problems with rectangular prisms, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
Surface Area of Rectangular Prisms

Practice: Surface Area of Rectangular Prisms

Question 1 of 5: Find the surface area of this rectangular prism:

Step 1. Unwrap the rectangular prism.

Step 2. Calculate the area of each shape in the net.

Since the net is made up of three pairs of identical rectangles, we only need to find the area of one rectangle from each pair.
ShapeArea
1
(Rectangle)
2
(Rectangle)
3
(Rectangle)
4
(Rectangle)
The same area as the area of shape
5
(Rectangle)
The same area as the area of shape
6
(Rectangle)
The same area as the area of shape

Step 3. Add up the area of all the shapes that make up the rectangular prism.

Awesome job! The surface area of the rectangular prism is .

CONCLUSION
Nice work, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?
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