108 LearnersLast updated on August 29, 2025
Surface Area of an Open Box
An open box is a three-dimensional shape with a rectangular base and four sides, but no top. The surface area of an open box is the total area covered by its outer surfaces. The surface area includes the area of the base and the four sides. In this article, we will learn about the surface area of an open box.
What is the Surface Area of an Open Box?
The surface area of an open box is the total area occupied by the boundary or surface of the box, excluding the top. It is measured in square units. An open box is a 3D shape with one flat base and four vertical sides. The surface area is calculated by finding the area of the base and adding the areas of the sides. Open boxes are commonly used for storage and packaging.
Surface Area of an Open Box Formula
An open box has a rectangular base and four sides.
The surface area consists of the base area and the lateral surface area (the area of the four sides).
Look at the box below to see its surface area, length(l), width(w), and height(h).
The surface area of an open box is calculated as: Surface Area = Base Area + Lateral Surface Area
Base Area of an Open Box
The base area of an open box is the area of the rectangular base.
It is found using the formula: Base Area = l × w
Here, l is the length of the base, and w is the width of the base.
Lateral Surface Area of an Open Box
The lateral surface area of an open box is the total area of its four sides.
It is calculated by finding the area of each side and summing them.
The formula for the lateral surface area is: Lateral Surface Area = 2(lh + wh) Where l is the length, w is the width, and h is the height of the box.
Volume of an Open Box
The volume of an open box shows how much space is inside it. It tells us how much space is available for storage.
The volume of an open box is calculated as: Volume = l × w × h (cubic units)
Confusion between Base Area and Lateral Surface Area
Students assume that the base area and the lateral surface area of an open box are the same. This confusion arises because both involve the dimensions of the box. Always remember that the base area is calculated using length and width, while the lateral surface area involves length, width, and height.
Mistake 1
Forgetting to Exclude the Top
Some students mistakenly calculate the surface area as if the box has a top. Remember, an open box does not have a top, so exclude it from your calculations.
Mistake 2
Using Incorrect Dimensions
A common mistake is using the wrong dimensions in formulas. Always double-check that you are using the correct length, width, and height.
Mistake 3
Incorrectly Summing Areas
Students often forget to sum all the side areas correctly. Make sure to calculate each side's area accurately and add them to find the total lateral surface area.
Mistake 4
Assuming All Sides Are Equal
Some students mistakenly believe all sides of the box are equal. Remember that in a rectangular box, length, width, and height can be different.
Mistake 5
Solved Examples of Surface Area of an Open Box
Find the surface area of an open box with a length of 10 cm, width of 5 cm, and height of 4 cm.
Surface Area = 130 cm²
Problem 1
Base Area = l × w = 10 × 5 = 50 cm² Lateral Surface Area = 2(lh + wh) = 2(10 × 4 + 5 × 4) = 2(40 + 20) = 2 × 60 = 120 cm² Surface Area = Base Area + Lateral Surface Area = 50 + 120 = 130 cm²
Find the surface area of an open box with a length of 8 cm, width of 6 cm, and height of 3 cm.
Explanation
Surface Area = 108 cm²
Problem 2
Base Area = l × w = 8 × 6 = 48 cm² Lateral Surface Area = 2(lh + wh) = 2(8 × 3 + 6 × 3) = 2(24 + 18) = 2 × 42 = 84 cm² Surface Area = Base Area + Lateral Surface Area = 48 + 84 = 132 cm²
An open box has a length of 12 cm, width of 7 cm, and height of 5 cm. Find the surface area.
Explanation
Surface Area = 274 cm²
Problem 3
Base Area = l × w = 12 × 7 = 84 cm² Lateral Surface Area = 2(lh + wh) = 2(12 × 5 + 7 × 5) = 2(60 + 35) = 2 × 95 = 190 cm² Surface Area = Base Area + Lateral Surface Area = 84 + 190 = 274 cm²
Find the surface area of an open box with length 9 cm, width 4 cm, and height 6 cm.
Explanation
Surface Area = 204 cm²
Problem 4
Base Area = l × w = 9 × 4 = 36 cm² Lateral Surface Area = 2(lh + wh) = 2(9 × 6 + 4 × 6) = 2(54 + 24) = 2 × 78 = 156 cm² Surface Area = Base Area + Lateral Surface Area = 36 + 156 = 192 cm²
The lateral surface area of an open box is 96 cm². If the length is 8 cm and the width is 3 cm, find the height.
Explanation
Height = 4 cm
It is the total area that covers the outside of the box, including the base and the four sides, but excluding the top.
1.What are the two types of surface areas in an open box?
2.How do you calculate the lateral surface area of an open box?
3.Is the base area part of the surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of an Open Box
Students often make mistakes while calculating the surface area of an open box, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
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