Surface Area of 3D Rectangle
2026-02-28 10:04 Diff
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Last updated on August 30, 2025

A 3D rectangle, also known as a rectangular prism or cuboid, is a 3-dimensional shape with six rectangular faces. The surface area of a 3D rectangle is the total area covered by its outer surface. It includes the areas of all six faces of the cuboid. In this article, we will learn about the surface area of a 3D rectangle.

What is the Surface Area of a 3D Rectangle?

The surface area of a 3D rectangle is the total area occupied by its external surfaces. It is measured in square units.

A 3D rectangle has six rectangular faces, forming a box-like shape.

Each face has a length and width, and the total surface area is the sum of the areas of all these faces.

Cuboids are often found in everyday objects like boxes, bricks, and books.

Surface Area of a 3D Rectangle Formula

A 3D rectangle has six faces, and the surface area is calculated by adding the areas of all these faces.

They are paired as opposite faces, each having the same area.

A cuboid has three pairs of opposite faces. If the dimensions are given as length (l), width (w), and height (h), the formula for the surface area is: Surface Area = 2(lw + lh + wh)

Finding the Surface Area of a 3D Rectangle

To calculate the surface area of a 3D rectangle, you must find the area of each pair of opposite faces and then add them up.

The formula is derived from adding the areas of the three unique faces and multiplying by two:

Surface Area = 2(lw + lh + wh)

Here, l is the length, w is the width, and h is the height of the cuboid.

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Example Calculations of Surface Area

Let's use an example to better understand the calculation. Consider a 3D rectangle with dimensions: 

Length = 4 cm 

Width = 3 cm 

Height = 5 cm

Using the formula: Surface Area = 2(lw + lh + wh) = 2(4×3 + 4×5 + 3×5) = 2(12 + 20 + 15) = 2×47 = 94 cm²

Volume of a 3D Rectangle

The volume of a 3D rectangle indicates how much space it occupies.

It is calculated using the product of its dimensions: length, width, and height.

The formula for the volume is: Volume = l×w×h (cubic units)

Mixing Up Dimensions

Students may confuse length, width, and height. Always ensure you correctly label and use these dimensions in the formula.

Problem 1

Given l = 6 cm, w = 4 cm, h = 3 cm. Use the formula: Surface Area = 2(lw + lh + wh) = 2(6×4 + 6×3 + 4×3) = 2(24 + 18 + 12) = 2×54 = 108 cm²

Okay, lets begin

Find the surface area of a 3D rectangle with dimensions: length 8 cm, width 5 cm, and height 7 cm.

Explanation

Surface Area = 262 cm²

Well explained 👍

Problem 2

Use the formula: Surface Area = 2(lw + lh + wh) = 2(8×5 + 8×7 + 5×7) = 2(40 + 56 + 35) = 2×131 = 262 cm²

Okay, lets begin

A box has dimensions of length 10 cm, width 6 cm, and height 4 cm. Find the surface area.

Explanation

Surface Area = 248 cm²

Well explained 👍

Problem 3

Use the formula: Surface Area = 2(lw + lh + wh) = 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24) = 2×124 = 248 cm²

Okay, lets begin

Calculate the surface area of a rectangular prism with length 9 cm, width 3 cm, and height 5 cm.

Explanation

Surface Area = 174 cm²

Well explained 👍

Problem 4

Surface Area = 2(lw + lh + wh) = 2(9×3 + 9×5 + 3×5) = 2(27 + 45 + 15) = 2×87 = 174 cm²

Okay, lets begin

The surface area of a 3D rectangle is 150 cm². If its length and width are 5 cm and 3 cm, respectively, find the height.

Explanation

Height = 5 cm

Well explained 👍

It is the total area that covers the outside of the 3D rectangle, including all its six rectangular faces.

1.How do you calculate the surface area of a 3D rectangle?

Use the formula: Surface Area = 2(lw + lh + wh), where l is length, w is width, and h is height.

2.What is the difference between surface area and volume?

Surface area measures the total area of the outside surfaces, while volume measures the space inside the 3D rectangle.

3.Can surface area be measured in cubic units?

No, surface area is measured in square units like cm², m², or in².

4.Are all sides of a 3D rectangle equal?

No, a 3D rectangle has three pairs of opposite faces, each pair having the same dimensions.

Common Mistakes and How to Avoid Them in the Surface Area of a 3D Rectangle

Students often make mistakes while calculating the surface area of a 3D rectangle, leading to incorrect answers. Below are some common mistakes and ways to avoid them.

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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.

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