107 LearnersLast updated on August 29, 2025
Surface Area of Octagon
An octagon is a 2-dimensional shape with eight sides. The surface area of an octagon refers to the total area covered by its shape. It does not have a curved surface like a 3D shape, but it has a flat surface area. In this article, we will learn about the surface area of an octagon.
What is the Surface Area of an Octagon?
The surface area of an octagon is the total area occupied by its boundary or surface. It is measured in square units. An octagon is a flat, 2D shape with eight straight sides and eight angles.
The surface area of an octagon is simply the area of the shape itself. Regular octagons have all sides and angles equal, while irregular octagons have sides and angles of different lengths and sizes.
Surface Area of an Octagon Formula
An octagon is a flat shape, and its surface area is simply its area.
For a regular octagon, the formula to find the surface area is straightforward.
Look at the octagon below to see its surface area and side length (s).
The formula for the surface area of a regular octagon is: Surface Area = 2(1 + √2)s²
Here, s is the side length of the octagon.
Regular vs. Irregular Octagons
A regular octagon has all sides and angles equal, making it easier to calculate the surface area using the formula.
An irregular octagon has sides and angles of different lengths and sizes, which means you need to break it down into smaller shapes (like triangles and rectangles) to find the total area.
Examples of Calculating Surface Area of Octagon
Below are examples of how to calculate the surface area of an octagon using the formula for a regular octagon. For irregular octagons, methods such as dividing into smaller shapes are used.
Importance of Knowing the Surface Area of an Octagon
Understanding the surface area of an octagon is useful in various applications, such as architectural designs, creating floor plans, or any situation where you need to cover or enclose a flat area with an octagonal shape. Knowing how to calculate it helps in planning and designing accurately.
Confusion between Regular and Irregular Octagons
Students assume all octagons are regular when calculating the surface area. This is incorrect, as irregular octagons require different methods to calculate their area. Always check if the octagon is regular or irregular before proceeding.
Mistake 1
Incorrect Use of the Formula
Some students mistakenly apply the formula for a regular octagon to an irregular one. Remember, the formula 2(1 + √2)s² only applies to regular octagons.
Mistake 2
Ignoring Unit Measurements
A common mistake is not paying attention to the units used, which can lead to incorrect area calculations. Always ensure the units are consistent when calculating the surface area.
Mistake 3
Forgetting to Divide Irregular Octagons into Simpler Shapes
Students often try to calculate the area of irregular octagons directly. Instead, divide the octagon into simpler shapes like triangles and rectangles to make calculations easier.
Mistake 4
Assuming All Sides are Equal in Irregular Octagons
Some students mistakenly believe all sides of an octagon are equal. In irregular octagons, side lengths can differ, which affects the surface area calculation.
Mistake 5
Solved Examples of Surface Area of Octagon
Find the surface area of a regular octagon with a side length of 4 cm.
Surface Area = 77.25 cm²
Problem 1
Given s = 4 cm. Use the formula: Surface Area = 2(1 + √2)s² = 2(1 + √2) × 4² = 2(1 + √2) × 16 = 77.25 cm²
Calculate the surface area of a regular octagon with a side length of 6 cm.
Explanation
Surface Area = 173.82 cm²
Problem 2
Use the formula: Surface Area = 2(1 + √2)s² = 2(1 + √2) × 6² = 2(1 + √2) × 36 = 173.82 cm²
An irregular octagon has side lengths of 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, 8 cm, 9 cm, and 10 cm. Find its approximate surface area by dividing it into simpler shapes.
Explanation
Surface Area ≈ 108 cm²
Problem 3
Divide the irregular octagon into triangles and rectangles. Calculate the area of each shape and sum them up to find the total surface area. The calculation might vary based on the specific arrangement of sides.
Find the surface area of a regular octagon with a side length of 5.5 cm.
Explanation
Surface Area = 146.69 cm²
Problem 4
Surface Area = 2(1 + √2)s² = 2(1 + √2) × 5.5² = 2(1 + √2) × 30.25 = 146.69 cm²
The surface area of a regular octagon is 200 cm². Find the side length.
Explanation
Side length ≈ 5.13 cm
It is the total area that covers the flat surface of an octagon.
1.What are the types of octagons?
2.What is the formula for the surface area of a regular octagon?
3.How do you find the surface area of an irregular octagon?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of an Octagon
Students often make mistakes while calculating the surface area of an octagon, 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
