103 LearnersLast updated on 29 August 2025
Surface Area of Regular Prism
A regular prism is a three-dimensional shape with two identical polygonal bases connected by rectangular faces. The surface area of a regular prism is the total area covered by its outer surfaces. The surface area includes both the lateral surface area, which is the area of the rectangular faces, and the areas of the bases. In this article, we will learn about the surface area of a regular prism.
What is the Surface Area of a Regular Prism?
The surface area of a regular prism is the total area occupied by the boundary or surface of the prism. It is measured in square units. A regular prism is a 3D shape with two identical polygonal bases and rectangular faces connecting these bases. The surface area of a regular prism consists of the lateral surface area and the base areas. Prisms can be classified based on their bases, such as triangular prisms, rectangular prisms, pentagonal prisms, etc.
Surface Area of a Regular Prism Formula
A regular prism has two types of surface areas: the lateral surface area and the total surface area.
Look at the regular prism below to see its surface area and base area.
A regular prism has two types of surface areas: Lateral Surface Area of a Regular Prism Total Surface Area of a Regular Prism
Lateral Surface Area of a Regular Prism
The area of the rectangular faces connecting the bases of the regular prism is known as the lateral surface area.
The lateral surface area of a regular prism is calculated using the formula:
Lateral Surface Area = Perimeter of the base × Height
Here, the perimeter of the base is the total length around one of the polygonal bases.
Total Surface Area of a Regular Prism
The total surface area of a regular prism is the sum of the lateral surface area and the area of the two bases.
It is calculated using the formula: Total Surface Area = Lateral Surface Area + 2 × Base Area
Where the base area is the area of one of the polygonal bases.
Volume of a Regular Prism
The volume of a regular prism indicates how much space is inside it. It is calculated by multiplying the area of the base by the height of the prism. The formula for the volume of a regular prism is: Volume = Base Area × Height
Confusion between Lateral Surface Area and Total Surface Area
Students sometimes assume that the lateral surface area and the total surface area of a regular prism are the same. This confusion often arises because both involve the height and the perimeter of the base. Always remember that the total surface area includes both the lateral surface and the base areas.
Mistake 1
Using Incorrect Base Area
Some students mistakenly use incorrect formulas or calculations for the base area. Ensure you know the correct formula for the base area, depending on the type of polygonal base (e.g., triangle, rectangle, etc.).
Mistake 2
Forgetting to Double the Base Area
A common mistake is forgetting to multiply the base area by two when calculating the total surface area. Remember that a prism has two bases, so always include both in your calculation.
Mistake 3
Confusing Height with Slant Height
In regular prisms, ensure you use the vertical height, not the slant height. The height is the perpendicular distance between the two bases.
Mistake 4
Misidentifying the Shape of the Base
Students may sometimes misidentify the shape of the base, leading to incorrect calculations. Ensure you correctly identify whether the base is a triangle, rectangle, pentagon, etc., to use the right formulas.
Mistake 5
Solved Examples of Surface Area of Regular Prism
Find the lateral surface area of a rectangular prism with a base perimeter of 20 cm and a height of 15 cm.
Lateral Surface Area = 300 cm²
Problem 1
Given base perimeter = 20 cm, height = 15 cm. Use the formula: Lateral Surface Area = Perimeter of the base × Height = 20 × 15 = 300 cm²
Find the total surface area of a triangular prism with a base area of 24 cm², base perimeter of 18 cm, and height of 12 cm.
Explanation
Total Surface Area = 432 cm²
Problem 2
Use the formula: Total Surface Area = Lateral Surface Area + 2 × Base Area Lateral Surface Area = Perimeter of the base × Height = 18 × 12 = 216 cm² Total Surface Area = 216 + 2 × 24 = 216 + 48 = 264 cm²
A pentagonal prism has a base perimeter of 30 cm, a base area of 50 cm², and a height of 10 cm.
Find the total surface area.
Explanation
Total Surface Area = 400 cm²
Problem 3
Use the TSA formula: Lateral Surface Area = Perimeter of the base × Height = 30 × 10 = 300 cm² Total Surface Area = Lateral Surface Area + 2 × Base Area = 300 + 2 × 50 = 300 + 100 = 400 cm²
Find the lateral surface area of a hexagonal prism with a base perimeter of 24 cm and a height of 9 cm.
Explanation
Lateral Surface Area = 216 cm²
Problem 4
Lateral Surface Area = Perimeter of the base × Height = 24 × 9 = 216 cm²
The base area of a rectangular prism is 60 cm², and its height is 20 cm. Find the total surface area if the base perimeter is 34 cm.
Explanation
Total Surface Area = 548 cm²
It is the total area that covers the outside of the prism, including its lateral surfaces and the bases.
1.What are the two types of surface area in a regular prism?
2.How do you find the base area of a regular prism?
3.Is the lateral surface area the same as the total surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Regular Prism
Students often make mistakes while calculating the surface area of a regular prism, which leads to incorrect 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
