101 LearnersLast updated on July 31st, 2025
Surface Area of Pentagonal Prism
A pentagonal prism is a 3-dimensional shape that has two pentagonal bases and rectangular lateral faces. The surface area of the pentagonal prism is the total area covered by its outer surface. The surface area includes both its lateral surface and its two bases. In this article, we will learn about the surface area of a pentagonal prism.
What is the Surface Area of a Pentagonal Prism?
The surface area of a pentagonal prism is the total area occupied by the boundary or surface of the prism. It is measured in square units.
A pentagonal prism is a 3D shape with two parallel pentagonal bases and five rectangular lateral faces. The surface area of a pentagonal prism includes the area of the lateral faces and the area of the two bases.
Surface Area of a Pentagonal Prism Formula
A pentagonal prism has a lateral surface and two pentagonal bases. The surface area consists of the lateral surface area and the area of the two bases.
A pentagonal prism has two types of surface areas: Lateral Surface Area of a Pentagonal Prism Total Surface Area of a Pentagonal Prism
Lateral Surface Area of a Pentagonal Prism
The area of the rectangular lateral faces of the prism, excluding its bases, is known as the lateral surface area of a pentagonal prism.
The formula for the LSA (Lateral Surface Area) of the pentagonal prism is given as: Lateral Surface Area = Perimeter of the base × Height
Here, the perimeter of the base is the sum of all sides of the pentagonal base, and the height is the perpendicular distance between the bases.
Total Surface Area of a Pentagonal Prism
The total area occupied by the pentagonal prism, including the area of the lateral surface and the area of the two pentagonal bases, is known as the total surface area of the pentagonal prism.
The total surface area of a pentagonal prism is calculated by using the formula:
Total surface area = Lateral Surface Area + 2 × Base Area
Where the Base Area is the area of one pentagonal base.
Volume of a Pentagonal Prism
The volume of a pentagonal prism shows how much space is inside it. It tells us how much space the prism can hold.
The volume of a pentagonal prism can be found by using the formula: Volume = Base Area × Height (cubic units)
Confusion between Lateral Surface Area and Total Surface Area
Students assume that the lateral surface area and the total surface area of a pentagonal prism are the same. This confusion arises because both involve the height and the perimeter of the base.
Always remember that the LSA is used for only the lateral faces, and the TSA includes the lateral surface and the bases.
Mistake 1
Using the wrong perimeter for the base
Some students mistakenly calculate the perimeter of the base incorrectly. Always ensure that the perimeter is the sum of all sides of the pentagonal base.
Mistake 2
Incorrect calculation of the base area
A common mistake is using the wrong formula or values for the base area. Ensure you use the correct formula to find the area of a pentagon, which can be calculated using specific known values like side length and apothem.
Mistake 3
Forgetting to include both bases in the total surface area
Students often calculate only one base area instead of both. Always include both bases when calculating the total surface area. Total surface area = lateral surface area + 2 × base area.
Mistake 4
Assuming lateral surface area and total surface area are the same
Some students mistakenly believe that lateral surface area and total surface area are the same, but in a pentagonal prism, they are different. So, use the appropriate formulas for each.
Mistake 5
Solved Examples of Surface Area of Pentagonal Prism
Find the lateral surface area of a pentagonal prism with a base perimeter of 20 cm and a height of 15 cm.
LSA = 300 cm²
Problem 1
Given the perimeter of the base = 20 cm, height = 15 cm. Use the formula: LSA = Perimeter of the base × Height = 20 × 15 = 300 cm²
Find the total surface area of a pentagonal prism with a base perimeter of 25 cm, a base area of 30 cm², and a height of 10 cm.
Explanation
TSA = 350 cm²
Problem 2
Use the formula: TSA = Lateral Surface Area + 2 × Base Area LSA = Perimeter of the base × Height = 25 × 10 = 250 cm² Base Area = 30 cm² TSA = 250 + 2 × 30 = 250 + 60 = 310 cm²
A pentagonal prism has a base perimeter of 18 cm, a base area of 24 cm², and a height of 12 cm. Find the total surface area.
Explanation
TSA = 336 cm²
Problem 3
Use the formula: TSA = Lateral Surface Area + 2 × Base Area LSA = Perimeter of the base × Height = 18 × 12 = 216 cm² Base Area = 24 cm² TSA = 216 + 2 × 24 = 216 + 48 = 264 cm²
Find the lateral surface area of a pentagonal prism with a base perimeter of 30 cm and a height of 8 cm.
Explanation
LSA = 240 cm²
Problem 4
LSA = Perimeter of the base × Height = 30 × 8 = 240 cm²
The height of a pentagonal prism is 14 cm, and its lateral surface area is 420 cm². Find the perimeter of the base.
Explanation
Perimeter = 30 cm
It is the total area that covers the outside of the pentagonal prism, including its lateral faces and the two bases.
1.What are the two types of surface area in a pentagonal prism?
2.How do you calculate the lateral surface area of a pentagonal 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 Pentagonal Prism
Students often make mistakes while calculating the surface area of a pentagonal prism, 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
