107 LearnersLast updated on August 16th, 2025
Surface Area of Cubes and Prisms
Cubes and prisms are 3-dimensional shapes with flat surfaces. The surface area of these shapes is the total area covered by their outer surfaces. For cubes, the surface area includes all six square faces, while for prisms, it includes the lateral faces and the two bases. In this article, we will learn about the surface areas of cubes and prisms.
What is the Surface Area of a Cube and a Prism?
The surface area of a cube or a prism 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 six equal square faces, while a prism is a polyhedron with two parallel, congruent bases connected by rectangular lateral faces. Cubes have identical faces, so the surface area is simply the area of one face multiplied by six. Prisms have various types, such as rectangular and triangular prisms. The surface area of a prism includes its lateral surface area and the area of its two bases.
Surface Area Formulas for Cubes and Prisms
Cubes and prisms have flat surfaces, and their surface areas are calculated by summing the areas of these surfaces. Surface Area of a Cube Surface Area of a Prism
Surface Area of a Cube
The surface area of a cube is the sum of the areas of its six square faces. The formula for the surface area of a cube is given as: Surface Area = 6a² square units Here, a is the length of one side of the cube.
Surface Area of a Prism
The total area occupied by a prism, including the area of its lateral surfaces and the area of its two bases, is known as the total surface area of a prism. The formula varies depending on the type of prism: For a rectangular prism: Total Surface Area = 2lw + 2lh + 2wh square units For a triangular prism: Total Surface Area = Base Area + Lateral Surface Area
Volume of a Cube and a Prism
The volume of a cube or a prism shows how much space is inside it. For a cube, the volume is calculated as: Volume = a³ cubic units For a prism, the volume is calculated by finding the base area and multiplying it by the height: Volume = Base Area × Height
Confusion between Cube and Prism Surface Areas
Students assume that the surface area formula for cubes applies to all prisms. Remember, cubes are a special type of prism, and each prism type has its own formula. Always use the formula specific to the shape.
Mistake 1
Using Incorrect Measurements
Some students mistakenly interchange dimensions like length, width, or height. Always verify the dimensions and use them correctly according to the shape's formula.
Mistake 2
Forgetting to Multiply by Two for Prisms
In prisms, students often forget to multiply the base and height dimensions by two when calculating surface areas. Ensure you account for both bases and all lateral faces.
Mistake 3
Assuming All Prisms are Rectangular
Some students mistakenly believe all prisms are rectangular. Remember, prisms can have different base shapes, like triangles. Use the appropriate formula based on the prism's base shape.
Mistake 4
Misidentifying the Base Area
Students sometimes confuse the base area with a side face area. Always identify the parallel congruent faces as the bases for accurate calculations.
Mistake 5
Solved Examples of Surface Area of Cubes and Prisms
Find the surface area of a cube with a side length of 4 cm.
Surface Area = 96 cm²
Problem 1
Given a = 4 cm. Use the formula: Surface Area = 6a² = 6 × (4)² = 6 × 16 = 96 cm²
Find the surface area of a rectangular prism with dimensions length = 5 cm, width = 3 cm, and height = 4 cm.
Explanation
Surface Area = 94 cm²
Problem 2
Use the formula: Total Surface Area = 2lw + 2lh + 2wh = 2(5 × 3) + 2(5 × 4) + 2(3 × 4) = 2(15) + 2(20) + 2(12) = 30 + 40 + 24 = 94 cm²
A triangular prism has a base area of 12 cm², a height of 10 cm, and three sides of the triangle as 5 cm, 4 cm, and 3 cm. Find the total surface area.
Explanation
Total Surface Area = 116 cm²
Problem 3
Calculate the lateral surface area: Lateral Surface Area = perimeter of base × height = (5 + 4 + 3) × 10 = 12 × 10 = 120 cm² Total Surface Area = Base Area × 2 + Lateral Surface Area = 12 × 2 + 120 = 24 + 120 = 144 cm²
Find the surface area of a cube with a side length of 6 cm.
Explanation
Surface Area = 216 cm²
Problem 4
Surface Area = 6a² = 6 × (6)² = 6 × 36 = 216 cm²
A rectangular prism has dimensions length = 7 cm, width = 2 cm, and height = 5 cm. Calculate its surface area.
Explanation
Surface Area = 122 cm²
It is the total area that covers the outside of the cube, including all six square faces.
1.What are the two types of prisms commonly studied?
2.How do you calculate the surface area of a rectangular prism?
3.What is the difference between a cube and a prism?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of Cubes and Prisms
Students often make mistakes while calculating the surface area of cubes and prisms, 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
: She has songs for each table which helps her to remember the tables
