Summarize this article:
129 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Hexagonal Prism
A hexagonal prism consists of two hexagonal bases and six rectangular lateral surfaces. The combined area of these six rectangular surfaces represents the lateral surface area of the hexagonal prism. Imagine a honeycomb structure, where the sides are the lateral surfaces, and the top and bottom faces are the hexagonal bases. The lateral surface area does not include the hexagonal bases.
What is the Lateral Surface Area of a Hexagonal Prism?
The lateral surface area of a hexagonal prism is the total area of the six rectangular faces that connect the two hexagonal bases of the prism.
Formula for Lateral Surface Area of a Hexagonal Prism
The lateral surface area (LSA) of a hexagonal prism can be found using the perimeter of the hexagonal base "P" and the height "h" of the prism.
The perimeter of a regular hexagon is given by P = 6a, where "a" is the side length of the hexagon.
The formula for the lateral surface area is: LSA = Ph = 6ah
How to Find Lateral Surface Area of a Hexagonal Prism
To find the Lateral Surface Area of a Hexagonal Prism, follow these steps:
Step 1: Determine the side length "a" of the hexagonal base and the height "h" of the prism.
Step 2: Calculate the perimeter of the hexagonal base as P = 6a.
Step 3: Use the equation LSA = Ph = 6ah to find the lateral surface area of the prism.
Step 4: Provide the calculated answer in square units.
Explore Our Programs
Common mistakes and how to avoid them in the Lateral Surface Area of a Hexagonal Prism.
There are common mistakes people make while calculating the lateral surface area of a hexagonal prism.
Some of them include:
Mistake 1
Incorrect calculation of the perimeter of the hexagonal base.
Students often forget that the perimeter of a regular hexagon is six times the side length.
Ensure you multiply the side length by six to get the correct perimeter.
Mistake 2
Confusing height with the side length of the hexagon.
The height "h" of the prism is the perpendicular distance between the two hexagonal bases, not the side length of the hexagon.
Always ensure to differentiate the two measurements.
Mistake 3
Not mentioning units with the numerical value.
It's crucial to mention units with your answer, even if the question does not specify them.
Use "square units" as a standard representation for area.
Mistake 4
Rounding in earlier steps.
Even correct rounding in intermediate steps can significantly affect the final answer.
Therefore, round off only the final answer to the required decimal places.
Mistake 5
Confusing lateral surface area with total surface area.
The lateral surface area covers only the rectangular surfaces, while the total surface area includes both the lateral surfaces and the two hexagonal bases.
Solved examples on Lateral Surface Area of a Hexagonal Prism
Problem 1
What is the lateral surface area of a hexagonal prism with a base side length of 4 cm and a height of 10 cm?
240 cm²
Explanation
Given: Side length = 4 cm, Height = 10 cm, Perimeter of base = 6 × 4 = 24 cm LSA = Ph = 24 × 10 = 240 cm²
Problem 2
If the side length of a hexagonal prism is 3 cm and the lateral surface area is 162 cmยฒ, find the height of the prism.
9 cm
Explanation
Given: Side length = 3 cm, LSA = 162 cm²
Perimeter of base = 6 × 3 = 18 cm
LSA = Ph = 18h 162 = 18h
h = 162/18
h = 9 cm
Problem 3
Calculate the lateral surface area of a hexagonal prism with a side length of 5 cm and a height of 12 cm.
360 cm²
Explanation
Given: Side length = 5 cm, Height = 12 cm, Perimeter of base = 6 × 5 = 30 cm
LSA = Ph = 30 × 12 = 360 cm²
Problem 4
Find the side length of a hexagonal prism if its height is 8 units and its lateral surface area is 288 square units.
6 units
Explanation
Given: Height = 8 units, LSA = 288 square units
Let the side length be "a".
Perimeter of base = 6a
LSA = 6a × 8 = 288
48a = 288,
a = 288/48 a = 6 units
Problem 5
The lateral surface area of a hexagonal prism is 150 cmยฒ. If its height is 5 cm, find the side length of the hexagonal base.
5 cm
Explanation
Let the side length be "a". Height = 5 cm, LSA = 150 cm²
Perimeter of base = 6a
LSA = 6a × 5 = 150
30a = 150
a = 150/30
a = 5 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 the same as the total surface area?
4.What is the relation between side length and perimeter of a hexagonal base?
5.How does the LSA change if the side length is doubled?
Important Glossary for Lateral Surface Area
- Regular hexagon: A polygon with six equal sides and angles.
- Perimeter: The total length around a 2D shape.
- Prism: A solid object with two identical ends and flat sides.
- Base: The face of a geometric shape on which it stands.
- Height: The perpendicular distance between the bases of a 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
