Surface Area of Octagon
2026-02-28 11:16 Diff
https://brightchamps.com/en-us/math/measurement/surface-area-of-octagon

175 Learners

Last updated on August 29, 2025

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.

Explore Our Programs

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.

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

Okay, lets begin

Calculate the surface area of a regular octagon with a side length of 6 cm.

Explanation

Surface Area = 173.82 cm²

Well explained 👍

Problem 2

Use the formula: Surface Area = 2(1 + √2)s² = 2(1 + √2) × 6² = 2(1 + √2) × 36 = 173.82 cm²

Okay, lets begin

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

Well explained 👍

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.

Okay, lets begin

Find the surface area of a regular octagon with a side length of 5.5 cm.

Explanation

Surface Area = 146.69 cm²

Well explained 👍

Problem 4

Surface Area = 2(1 + √2)s² = 2(1 + √2) × 5.5² = 2(1 + √2) × 30.25 = 146.69 cm²

Okay, lets begin

The surface area of a regular octagon is 200 cm². Find the side length.

Explanation

Side length ≈ 5.13 cm

Well explained 👍

It is the total area that covers the flat surface of an octagon.

1.What are the types of octagons?

There are regular octagons, which have equal sides and angles, and irregular octagons, which have sides and angles of different lengths and sizes.

2.What is the formula for the surface area of a regular octagon?

The formula is Surface Area = 2(1 + √2)s², where s is the side length.

3.How do you find the surface area of an irregular octagon?

Divide the octagon into simpler shapes like rectangles and triangles, calculate each area, and sum them up.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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.

What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math

▶

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