Surface Area of Rectangular Solid
2026-02-28 10:49 Diff
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Last updated on August 5, 2025

A rectangular solid, also known as a rectangular prism, is a 3-dimensional shape with six faces, all of which are rectangles. The surface area of a rectangular solid is the total area covered by its outer surface. In this article, we will learn about the surface area of a rectangular solid.

What is the Surface Area of a Rectangular Solid?

The surface area of a rectangular solid is the total area occupied by the boundary or surface of the shape. It is measured in square units.

A rectangular solid is a 3D shape that has length, width, and height. Each of its faces is a rectangle, and it has six faces in total.

To find the surface area, you calculate the area of each face and then sum them up. A rectangular solid can also be referred to as a box.

Surface Area of a Rectangular Solid Formula

A rectangular solid has six rectangular faces, and its surface area includes the area of each of these faces. Look at the rectangular solid below to see its surface area, length (l), width (w), and height (h).

A rectangular solid has six faces with the following formula for the surface area:

Surface Area = 2(lw + lh + wh) square units

Calculating the Surface Area of a Rectangular Solid

To calculate the surface area of a rectangular solid, we need to find the area of each of its six rectangular faces and sum them up. The formula for the surface area is:

Surface Area = 2(lw + lh + wh)

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

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Example of Surface Area Calculation

Consider a rectangular solid with a length of 5 cm, a width of 3 cm, and a height of 4 cm.

To find the total surface area, we use the formula:

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

Volume of a Rectangular Solid

The volume of a rectangular solid shows how much space is inside it. It tells us the capacity of the solid or how much it can hold.

The volume can be found by using the formula: Volume = l × w × h (cubic units)

Confusion between Surface Area and Volume

Students sometimes confuse the formulas for surface area and volume. Remember that surface area involves adding the areas of all the faces, while volume is the product of length, width, and height.

Problem 1

Given l = 7 cm, w = 4 cm, h = 3 cm. Use the formula: Surface Area = 2(lw + lh + wh) = 2(7 × 4 + 7 × 3 + 4 × 3) = 2(28 + 21 + 12) = 2 × 61 = 122 cm²

Okay, lets begin

Find the surface area of a rectangular solid with a length of 5 cm, width of 6 cm, and height of 2 cm.

Explanation

Surface Area = 104 cm²

Well explained 👍

Problem 2

Use the formula: Surface Area = 2(lw + lh + wh) = 2(5 × 6 + 5 × 2 + 6 × 2) = 2(30 + 10 + 12) = 2 × 52 = 104 cm²

Okay, lets begin

A rectangular solid has a length of 8 cm, width of 5 cm, and height of 4 cm. Find the surface area.

Explanation

Surface Area = 184 cm²

Well explained 👍

Problem 3

Use the formula: Surface Area = 2(lw + lh + wh) = 2(8 × 5 + 8 × 4 + 5 × 4) = 2(40 + 32 + 20) = 2 × 92 = 184 cm²

Okay, lets begin

Find the surface area of a rectangular solid with a length of 6 cm, width of 3 cm, and height of 2 cm.

Explanation

Surface Area = 72 cm²

Well explained 👍

Problem 4

Surface Area = 2(lw + lh + wh) = 2(6 × 3 + 6 × 2 + 3 × 2) = 2(18 + 12 + 6) = 2 × 36 = 72 cm²

Okay, lets begin

The surface area of a rectangular solid is 150 cm². If the length is 5 cm and the width is 3 cm, find the height.

Explanation

Height = 5 cm

Well explained 👍

It is the total area that covers the outside of the rectangular solid, including all its rectangular faces.

1.What is the formula for the surface area of a rectangular solid?

The formula for the surface area is 2(lw + lh + wh), where l is the length, w is the width, and h is the height.

2.How do you calculate the volume of a rectangular solid?

The volume is calculated by multiplying the length, width, and height: Volume = l × w × h.

3.Are all faces of a rectangular solid the same size?

No, the faces of a rectangular solid can have different sizes, but opposite faces are always the same size.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

Common Mistakes and How to Avoid Them in the Surface Area of a Rectangular Solid

Students often make mistakes while calculating the surface area of a rectangular solid, which leads to wrong answers. Below are some common mistakes and the 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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