102 LearnersLast updated on August 5th, 2025
Surface Area of Right Prism
A right prism is a 3-dimensional geometric figure with two congruent and parallel bases. The surface area of a right prism is the total area that covers its outer surface. This area comprises the lateral surface area, which includes all the rectangular faces connecting the bases, and the base areas themselves. In this article, we will learn about the surface area of a right prism.
What is the Surface Area of a Right Prism?
The surface area of a right prism is the total area occupied by its outer surface. It is measured in square units. A right prism is a 3D shape with two parallel, congruent bases and rectangular lateral faces.
The surface area of a right prism includes both the lateral surface area and the area of the two bases. Right prisms can have various types of polygonal bases, such as triangular, rectangular, or hexagonal.
Surface Area of a Right Prism Formula
A right prism has lateral surfaces and two base areas. Look at the right prism below to see its surface area, height (h), and the perimeter (P) of its base.
A right prism has two types of surface areas: Lateral Surface Area of a Right Prism Total Surface Area of a Right Prism
Lateral Surface Area of a Right Prism
The lateral surface area of a right prism is the total area of all the rectangular faces connecting the two bases.
The formula for the Lateral Surface Area (LSA) of a right prism is given as:
Lateral Surface Area = Perimeter of base × height
Here, P is the perimeter of the base of the prism. h is the height of the prism.
Total Surface Area of a Right Prism
The total surface area of a right prism is the sum of the lateral surface area and the area of the two bases.
The total surface area of a right prism is calculated by using the formula:
Total Surface Area = Lateral Surface Area + 2 × Base Area
Where P is the perimeter of the base. h is the height of the prism. B is the area of the base.
Derivation of the Total Surface Area of a Right Prism To find the total surface area, calculate the lateral surface area and add the areas of the two bases.
Consider a right prism with height (h), perimeter of the base (P), and base area (B).
Total surface area of a right prism = lateral surface area + 2 × base area Lateral surface area = P × h
Substituting into the total surface area, Total Surface Area, T = P × h + 2B
Volume of a Right Prism
The volume of a right prism shows how much space it occupies. It indicates the capacity of the prism.
The volume of a right prism can be found using the formula: Volume = Base Area × Height (cubic units)
Confusion between LSA and TSA
Students sometimes confuse the lateral surface area (LSA) with the total surface area (TSA) of a right prism. Remember, LSA only involves the lateral faces, while TSA includes both the lateral surface and the base areas.
Mistake 1
Using incorrect dimensions
Some students mistakenly use incorrect dimensions for height or perimeter when finding the lateral surface area. Ensure the correct values are used as per the given dimensions.
Mistake 2
Omitting base areas in TSA
A common mistake is calculating only the lateral surface and forgetting to add the areas of the bases. Always include both base areas in the total surface area calculation.
Mistake 3
Misidentifying the base shape
Students sometimes misidentify the shape of the base, leading to incorrect perimeter or area calculations. Always confirm the base shape before proceeding with calculations.
Mistake 4
Assuming LSA includes base areas
Some students mistakenly believe the lateral surface area includes base areas, but in a right prism, they are separate. Use the correct formula for both.
Mistake 5
Solved Examples of Surface Area of Right Prism
Find the lateral surface area of a right prism with a triangular base of perimeter 12 cm and height of 5 cm.
LSA = 60 cm²
Problem 1
Given P = 12 cm, h = 5 cm. Use the formula: LSA = P × h = 12 × 5 = 60 cm²
Find the total surface area of a right prism with a rectangular base of perimeter 20 cm, base area of 24 cm², and height of 4 cm.
Explanation
TSA = 112 cm²
Problem 2
Use the formula: TSA = LSA + 2 × B = P × h + 2B = 20 × 4 + 2 × 24 = 80 + 48 = 128 cm²
A right prism has a hexagonal base with perimeter 30 cm and base area 45 cm². Find the total surface area if the height is 10 cm.
Explanation
TSA = 390 cm²
Problem 3
Use the TSA formula: TSA = LSA + 2 × B = P × h + 2B = 30 × 10 + 2 × 45 = 300 + 90 = 390 cm²
Find the lateral surface area of a right prism with a square base of perimeter 16 cm and height 7 cm.
Explanation
LSA = 112 cm²
Problem 4
LSA = P × h = 16 × 7 = 112 cm²
The lateral surface area of a right prism is 96 cm² and the height is 8 cm. Find the perimeter of the base.
Explanation
Perimeter = 12 cm
It is the total area that covers the outer surface of the right prism, including its lateral sides and the bases.
1.What are the two types of surface area in a right prism?
2.What is the difference between lateral surface area and total surface area?
3.Does lateral surface area include the base areas?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Right Prism
Students often make mistakes while calculating the surface area of a right prism, leading to incorrect answers. Below are some common mistakes and 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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