# Surface Area of a Box

Welcome to our Surface Area of a Box page.

We explain how to find the surface area of a cuboid, or box, and provide a quick calculator to work it out for you, step-by-step.

Our calculator will find the surface area of both closed and open boxes.

There are also lots of worked examples and some worksheets for you to practice this skill.

### Surface Area of a Box Calculator

Surface Area of a Box Calculator ### Surface Area of a Box Examples

#### Surface Area of a Box Example 1

Find the surface area of the box below. The box has the following dimensions:

• Length: 7 cm
• Width: 3 cm
• Height: 5 cm

The surface area of the box is:

$A = 2lw + 2lh + 2wh \;$

where l is the length, w is the width, and h is the height of the box

So if we substitute the values of the length and width into this equation, we get: $A = 2 \cdot 7 \cdot 3 + 2 \cdot 7 \cdot 5 + 2 \cdot 3 \cdot 5 = 42 + 70 + 30 = 142$

The surface area of the box is 142 cm2.

#### Surface Area of a Box Example 2

Find the surface area of the box below. The box has the following dimensions:

• Length (l):12 in
• Width (w): 5 in
• Height (h): 3 in

The surface area of the box is:

$A = 2lw + 2lh + 2wh \;$

So if we substitute the values of the length and width into this equation, we get: $A = 2 \cdot 12 \cdot 5 + 2 \cdot 12 \cdot 3 + 2 \cdot 5 \cdot 3 = 120 + 72 + 30 = 222$

The surface area of the box is 222 in2.

#### Surface Area of a Box Example 3

Find the surface area of the box below, giving your answer to 1 decimal place. The box has the following dimensions:

• Length (l): 5.6 cm
• Width (w): 4.3 cm
• Height (h): 2.5 cm

The surface area of the box is:

$A = 2lw + 2lh + 2wh \;$

So if we substitute the values of the length and width into this equation, we get: $A = 2 \cdot 5.6 \cdot 4.3 + 2 \cdot 5.6 \cdot 2.5 + 2 \cdot 4.3 \cdot 2.5 = 48.16 + 28 + 21.5 = 97.66$

The surface area of the box is 97.7 cm2 to 1 decimal place.

#### Surface Area of a Box Example 4

Find the surface area of the open box below. The box has the following dimensions:

• Length (l): 6 in
• Width (w): 3 ½ in
• Height (h): 2 ½ in

The formula for the surface area of an open box is:

$A = lw + 2lh + 2wh \;$

So if we substitute the values of the length and width into this equation, we get: $A = 6 \cdot 3 {1 \over 2} + 2 \cdot 6 \cdot 2 {1 \over 2} + 2 \cdot 3 {1 \over 2} \cdot 2 {1 \over 2} = 21 + 30 + 17 {1 \over 2} = 68 {1 \over 2}$

The surface area of the box is 68 ½ in2.

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