113 LearnersLast updated on August 5th, 2025
Surface Area of Rectangular Solid
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.
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.
Mistake 1
Forgetting to double the sum of face areas
Some students forget that the formula requires doubling the sum of the face areas because each face has a parallel opposite face. Always use the formula 2(lw + lh + wh).
Mistake 2
Using incorrect measurements
A common mistake is using incorrect or mismatched measurements for length, width, or height. Ensure all measurements are in the same unit before using them in calculations.
Mistake 3
Mixing up length, width, and height
Students often mix up which side is length, width, or height, especially if the solid is not oriented in the usual way. Label each side clearly before performing calculations.
Mistake 4
Neglecting to include all face areas
Some students calculate only part of the surface area, forgetting one or more faces. Ensure that all six faces are accounted for in the calculation.
Mistake 5
Solved Examples of Surface Area of Rectangular Solid
Find the surface area of a rectangular solid with a length of 7 cm, width of 4 cm, and height of 3 cm.
Surface Area = 94 cm²
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
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
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
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
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
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
Problem 4
Surface Area = 2(lw + lh + wh) = 2(6 × 3 + 6 × 2 + 3 × 2) = 2(18 + 12 + 6) = 2 × 36 = 72 cm²
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
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?
2.How do you calculate the volume of a rectangular solid?
3.Are all faces of a rectangular solid the same size?
4.What unit is surface area measured in?
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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: She has songs for each table which helps her to remember the tables
