Surface Area of Cubes & Rectangular Prisms and Gift Wrap 🎁

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Surface Area of Cubes & Rectangular Prisms and Gift Wrap 🎁

Surface Area of Cubes & Rectangular Prisms and Gift Wrap 🎁

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:

surfacearea = sum of faceareas

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.

Surface Area of Cubes & Rectangular Prisms Calculator

What is your shape?

$s$

$l$

$w$

$h$

$r$

$h$

$s$

$r$

$s$

$h$

$s=$

$l=$

$w=$

$h=$

$r=$

$h=$

$h=$

$s=$

$r=$

$s=$

Step 1. Unwrap the cube.

This gives us our net:

$s$

$l$

$w$

$h$

$r$

$h$

$s$

$r$

$s$

$h$

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 🎉.

$s$

$l$

$w$

$h$

$r$

$h$

$r$

$s$

$s$

$h$

Shape

Area

1

(Square)

$A =s_{2}=(0)_{2}=0 $

2

(Square)

$A =same as shape 1=0 $

3

(Square)

$A =same as shape 1=0 $

4

(Square)

$A =same as shape 1=0 $

5

(Square)

$A =same as shape 1=0 $

6

(Square)

$A =same as shape 1=0 $

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

$SA =0 +0 +0 +0 +0 +0 =6×0 =0 $

The surface area of this cube is $SA=0$.

Key Steps 🗝 How to Find Surface Area of Cubes and Rectangular Prisms

Shape

Step 1. Unwrap the cube.

$s$

$l$

$w$

$h$

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$undefined$

$undefined$

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$undefined$

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

$s$

$l$

$w$

$h$

$undefined$

$undefined$

$undefined$

$undefined$

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Squares 1 - 6

$A=s_{2}$

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

$SA=6×s_{2} $

Continue to explore how to find the surface area of cubes and rectangular prisms in more detail ✨.

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 $6$ identical squares.So, we only need to find the area of one of the squares ($A=s_{2}$), and add it $6$ times (or multiply it by $6$ ) to get the total surface area!$SAof cube =s_{2}+s_{2}+s_{2}+s_{2}+s_{2}+s_{2}=6s_{2} $Let's unwrap some more cubes to find their surface area!

Let's start here - find the surface area of this cube:

What is your shape?

$3$

$l$

$w$

$h$

$r$

$h$

$s$

$r$

$s$

$h$

Step 1. Unwrap the cube.

This gives us our net:

$3$

$l$

$w$

$h$

$r$

$h$

$s$

$r$

$s$

$h$

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 🎉.

$3$

$l$

$w$

$h$

$r$

$h$

$r$

$s$

$s$

$h$

Shape

Area

1

(Square)

$A =s_{2}=(3)_{2}=9 $

2

(Square)

$A =same as shape 1=9 $

3

(Square)

$A =same as shape 1=9 $

4

(Square)

$A =same as shape 1=9 $

5

(Square)

$A =same as shape 1=9 $

6

(Square)

$A =same as shape 1=9 $

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

$SA =9 +9 +9 +9 +9 +9 =6×9 =54 $

The surface area of this cube is $SA=54$.

Nice work! Try another one:

What is your shape?

$4$

$l$

$w$

$h$

$r$

$h$

$s$

$r$

$s$

$h$

Step 1. Unwrap the cube.

This gives us our net:

$4$

$l$

$w$

$h$

$r$

$h$

$s$

$r$

$s$

$h$

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 🎉.

$4$

$l$

$w$

$h$

$r$

$h$

$r$

$s$

$s$

$h$

Shape

Area

1

(Square)

$A =s_{2}=(4)_{2}=16 $

2

(Square)

$A =same as shape 1=16 $

3

(Square)

$A =same as shape 1=16 $

4

(Square)

$A =same as shape 1=16 $

5

(Square)

$A =same as shape 1=16 $

6

(Square)

$A =same as shape 1=16 $

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

$SA =16 +16 +16 +16 +16 +16 =6×16 =96 $

The surface area of this cube is $SA=96$.

Practice with some additional problems or keep scrolling to learn more about how to find the surface area of rectangular prisms.

Practice: Surface Area of Cubes

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

$2$

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Step 1. Unwrap the cube.

$2$

$undefined$

$undefined$

$undefined$

$undefined$

$undefined$

$undefined$

$undefined$

$undefined$

$undefined$

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

$2$

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$undefined$

$undefined$

$undefined$

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$undefined$

$undefined$

$undefined$

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.

Shape

Area

1

(Square)

$A$$=$$s_{2}$$=$

$_{2}$

$=$

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

$SA$$=$$4 +4 +4 +4 +4 +4 $$=$$6×4 $$=$

Awesome job! The surface area of the cube is $SA=24$.

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!$SAof rectangular prism =(2×l×h)+(2×h×w)+(2×l×w)=2lh+2hw+2lw $Let’s unwrap some more rectangular prisms and find their total surface areas!

Let's start here - find the surface area of this rectangular prism:

What is your shape?

$s$

$5$

$4$

$3$

$r$

$h$

$s$

$r$

$s$

$h$

Step 1. Unwrap the rectangular prism.

This gives us our net:

$s$

$5$

$4$

$3$

$r$

$h$

$s$

$r$

$s$

$h$

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 🎉.

$s$

$5$

$4$

$3$

$r$

$h$

$r$

$s$

$s$

$h$

Shape

Area

1

(Rectangle)

$A =l×h=5×3=15 $

2

(Rectangle)

$A =w×h=4×3=12 $

3

(Rectangle)

$A =l×w=5×4=20 $

4

(Rectangle)

$A =same as shape 2=12 $

5

(Rectangle)

$A =same as shape 1=15 $

6

(Rectangle)

$A =same as shape 3=20 $

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