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135 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Right Prism
A right prism consists of two congruent polygonal bases and several rectangular lateral faces. The lateral surface area represents the sum of the areas of these rectangular faces. Consider a rectangular box with a lid and a base. The walls of the box form the lateral surface, which is equal to the lateral surface area of the right prism. The bases are not included in the lateral surface area calculation.
How to Find Lateral Surface Area of a Right Prism
To find the lateral surface area of a right prism, follow these steps:
Step 1: Note the given parameters such as the perimeter of the base and the height of the prism.
Step 2: Ensure that all measurements are in the same unit before performing calculations.
Step 3: Use the equation Area = P × h to find the lateral surface area of the prism.
Step 4: Provide the calculated answer in square units.
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Common Mistakes and How to Avoid Them in the Lateral Surface Area of a Right Prism.
There are a few typical mistakes people make while calculating the lateral surface area of a right prism.
Some of them are listed below:
Mistake 1
Confusing the total surface area with the lateral surface area.
The lateral surface area includes only the rectangular faces, not the base areas.
The total surface area includes both the lateral surface area and the area of the bases.
Mistake 2
Incorrect calculation of the perimeter of the base.
Ensure you accurately calculate the perimeter of the base by summing all the side lengths of the polygonal base.
Mistake 3
Not mentioning the units with the numerical value.
Always include the units with your answer, even if the question doesn't specify them.
It's preferable to write “square units” for the standard representation of an area value.
Mistake 5
Using incorrect formulae for the lateral surface area.
Ensure you are using the correct formula for a right prism, which is Area = P × h, where P is the perimeter of the base.
Solved Examples on Lateral Surface Area of a Right Prism
Problem 1
What is the lateral surface area of a right prism with a triangular base whose perimeter is 15 cm and height is 10 cm?
150 cm²
Explanation
Given: Perimeter of base = 15 cm, Height = 10 cm
LSA = P × h = 15 × 10 = 150 cm²
Problem 2
If the perimeter of the base of a right prism is q cm and the height is 8 cm with a lateral surface area of 64 cmยฒ, find the value of q.
8 cm
Explanation
Given: Perimeter (P) = q cm Height (h) = 8 cm
LSA = 64 cm²
Using the formula: LSA = P × h 64 = q × 8
Solve for q: q = 64 / 8
q = 8 cm
Problem 3
Calculate the lateral surface area of a right prism with a square base where each side is 5 cm and the height of the prism is 7 cm.
140 cm²
Explanation
Given: Side of base = 5 cm
Perimeter of base = 4 × 5 = 20 cm
Height (h) = 7 cm
LSA = P × h = 20 × 7 = 140 cm²
Problem 4
Evaluate the height of a right prism if its base perimeter is 12 units and its lateral surface area is 96 square units.
8 units
Explanation
Given: Perimeter of base (P) = 12 units
Lateral surface area (LSA) = 96 square units
Let the height = h.
Using the LSA formula: LSA = P × h 96 = 12 × h
Solve for h: h = 96 / 12
h = 8 units
Problem 5
The lateral surface area of a right prism is 330 cmยฒ. If its base perimeter is 22 cm, find its height.
15 cm
Explanation
Let the height be “h” cm. Given: LSA = 330 cm²
Perimeter of base (P) = 22 cm
Using the formula: LSA = P × h
330 = 22 × h
Solve for h: h = 330 / 22
h = 15 cm
FAQโs on Lateral Surface Area
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area.
3.Is the lateral surface area and the total surface area the same?
4.What is the relation between the lateral surface area and the perimeter of the base?
5.How does the lateral surface area change if the height is doubled?
Important Glossary for Lateral Surface Area
- Right Prism: A three-dimensional geometric figure with two congruent polygonal bases and rectangular lateral faces perpendicular to the base.
- Perimeter: The total length of the sides of a polygon.
- Height: The perpendicular distance between the two bases of a right prism.
- Rectangular Faces: The lateral faces of a right prism, which are rectangles.
- Lateral Surface: The sum of the areas of the rectangular faces of a right prism.
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
