Surface Area of Cubes and Rectangular Prisms
2026-02-28 13:24 Diff
https://brightchamps.com/en-us/math/measurement/surface-area-of-cubes-and-rectangular-prisms

174 Learners

Last updated on August 30, 2025

Cubes and rectangular prisms are 3-dimensional shapes with flat faces. The surface area of these shapes is the total area covered by their outer surfaces. For cubes, all faces are equal squares, while rectangular prisms have opposite faces that are equal rectangles. In this article, we will learn about the surface area of cubes and rectangular prisms.

What is the Surface Area of Cubes and Rectangular Prisms?

The surface area of cubes and rectangular prisms is the total area occupied by the boundary or surface of these shapes.

It is measured in square units.

A cube is a 3D shape with all sides equal, making it a special type of rectangular prism.

A rectangular prism has six rectangular faces, with opposite faces being identical.

Surface areas are classified based on the shape: the surface area of a cube and the surface area of a rectangular prism.

Surface Area of Cubes and Rectangular Prisms Formula

Cubes and rectangular prisms have straightforward surface area formulas due to their regular shapes.

For a cube with side length s, the surface area is:

Surface Area of a Cube = 6s²

For a rectangular prism with length l, width w, and height h, the surface area is:

Surface Area of a Rectangular Prism = 2(lw + lh + wh)

Surface Area of a Cube

The surface area of a cube is the total area covered by all six of its identical square faces.

Each face of a cube is a square with the side length s.

The formula to calculate the surface area of a cube is:

Surface Area = 6s² Where s is the length of a side of the cube.

Explore Our Programs

Surface Area of a Rectangular Prism

The total area occupied by the rectangular prism, including the area of all six rectangular faces, is known as the surface area of the rectangular prism.

The formula for calculating the surface area is:

Surface Area = 2(lw + lh + wh)

Where l is the length, w is the width, and h is the height of the rectangular prism.

Volume of Cubes and Rectangular Prisms

The volume of these shapes shows how much space is inside them.

For a cube, the volume is the cube of its side length, and for a rectangular prism, it’s the product of its dimensions.

The formulas are:

Volume of a Cube = s³ Volume of a Rectangular Prism = lwh

Confusing volume with surface area

Students sometimes mix up the concept of volume and surface area. Remember, volume measures the space inside, while surface area measures the outer covering.

Problem 1

Given s = 4 cm. Use the formula: Surface Area = 6s² = 6 × (4)² = 6 × 16 = 96 cm²

Okay, lets begin

Find the surface area of a rectangular prism with dimensions 3 cm by 4 cm by 5 cm.

Explanation

Surface Area = 94 cm²

Well explained 👍

Problem 2

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

Okay, lets begin

A cube has a side length of 7 cm. Find its surface area.

Explanation

Surface Area = 294 cm²

Well explained 👍

Problem 3

Use the formula: Surface Area = 6s² = 6 × (7)² = 6 × 49 = 294 cm²

Okay, lets begin

Find the surface area of a rectangular prism with length 10 cm, width 4 cm, and height 6 cm.

Explanation

Surface Area = 248 cm²

Well explained 👍

Problem 4

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

Okay, lets begin

The surface area of a cube is 150 cm². Find the side length.

Explanation

Side Length = 5 cm

Well explained 👍

It is the total area that covers the outside of the cube across all six of its equal square faces.

1.How do you calculate the surface area of a rectangular prism?

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 a cube and a rectangular prism?

A cube has all sides equal, making it a special type of rectangular prism, while a rectangular prism has different lengths for its dimensions.

3.Are surface area and volume the same?

No, surface area measures the total area of the outer surface, while volume measures the space inside the shape.

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 Cubes and Rectangular Prisms

Students often make mistakes while calculating the surface area of cubes and rectangular prisms, leading to incorrect answers. Below are some common mistakes and the ways to avoid them.

What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math

▶

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

: She has songs for each table which helps her to remember the tables