Area of Octagon
2026-02-28 13:00 Diff
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Last updated on September 17, 2025

Area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of the octagon.

What is the Area of an Octagon?

An octagon is a polygon with eight sides and eight angles. A regular octagon has all sides of equal length and all interior angles are equal. The area of the octagon is the total space it encloses.

Area of the Octagon Formula

To find the area of a regular octagon, we use the formula: Area = 2 × (1 + √2) × a², where 'a' is the length of a side. Let's understand how this formula is derived.

Derivation of the formula: A regular octagon can be divided into 8 isosceles triangles by drawing lines from the center to each vertex. For one triangle, the base is the side 'a' of the octagon, and the height can be found using trigonometry. The area of one triangle is (1/2) × base × height. The total area of the octagon is 8 times the area of one triangle, which simplifies to 2 × (1 + √2) × a².

How to Find the Area of an Octagon?

The area of a regular octagon can be found using the side length. Here’s the method: Method Using the Side Length If the side length 'a' is given, use the formula Area = 2 × (1 + √2) × a².

For example, if the side length is 5 cm, what will be the area of the octagon? Area = 2 × (1 + √2) × 5² = 2 × (1 + √2) × 25 = 2 × (1 + 1.414) × 25 = 2 × 2.414 × 25 = 120.7 cm² The area of the octagon is approximately 120.7 cm².

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Unit of Area of Octagon

We measure the area of an octagon in square units. The measurement depends on the system used: In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).

In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).

Special Cases or Variations for the Area of Octagon

A regular octagon has equal sides and equal angles, making the formula for its area consistent. However, for irregular octagons, different methods may be required:

Case 1: Regular Octagon Use the formula Area = 2 × (1 + √2) × a², where 'a' is the side length.

Case 2: Irregular Octagon An irregular octagon requires dividing it into known shapes, such as triangles or rectangles, and summing their areas.

Tips and Tricks for Area of Octagon

To ensure correct results while calculating the area of an octagon, consider these tips and tricks:

  • Ensure all sides are equal for a regular octagon.
     
  • Use trigonometry for height if calculating manually.
     
  • For irregular octagons, divide into simpler shapes.

Common Mistakes and How to Avoid Them in Area of Octagon

It is common for individuals to make mistakes while finding the area of an octagon. Here are some common mistakes:

Problem 1

The side length of a regular octagon-shaped tile is given as 12 cm. What will be the area?

Okay, lets begin

The area is approximately 695.4 cm².

Explanation

Here, the side length 'a' is 12 cm.

The area of the octagon = 2 × (1 + √2) × a² = 2 × (1 + √2) × 12² = 2 × 2.414 × 144 = 695.4 cm².

Well explained 👍

Problem 2

What will be the area of a regular octagon if the side length is 7 m?

Okay, lets begin

The area is approximately 284.6 m².

Explanation

If the side length is 7 m, the formula Area = 2 × (1 + √2) × a² is used.

So, the area = 2 × (1 + √2) × 7² = 2 × 2.414 × 49 = 284.6 m².

Well explained 👍

Problem 3

Calculate the area of a regular octagon with a side length of 10 cm.

Okay, lets begin

The area is approximately 482.8 cm².

Explanation

To find the area, use the formula Area = 2 × (1 + √2) × a².

Here, a is 10 cm. So, Area = 2 × (1 + √2) × 10² = 2 × 2.414 × 100 = 482.8 cm².

Well explained 👍

Problem 4

Find the area of a regular octagon with a side length of 15 inches.

Okay, lets begin

The area is approximately 1309.6 in².

Explanation

Using the side length of 15 in, the area is calculated as Area = 2 × (1 + √2) × 15² = 2 × 2.414 × 225 = 1309.6 in².

Well explained 👍

Problem 5

Help Lisa find the area of her regular octagon-shaped garden if each side is 8 m long.

Okay, lets begin

The area is approximately 309.0 m².

Explanation

The side length is 8 m.

Use the formula Area = 2 × (1 + √2) × a² = 2 × 2.414 × 64 = 309.0 m².

Well explained 👍

FAQs on Area of Octagon

1.Can the area of an octagon be negative?

No, the area of an octagon can never be negative. The area of any shape will always be positive.

2.How to find the area of an octagon if the side length is given?

If the side length is given, the area can be found using the formula Area = 2 × (1 + √2) × a².

3.How to find the area of an irregular octagon?

For an irregular octagon, divide it into known shapes like triangles or rectangles and sum their areas.

4.How is the perimeter of an octagon calculated?

The perimeter of a regular octagon is calculated using the formula P = 8 × a, where 'a' is the side length.

5.What is meant by the area of an octagon?

The area of an octagon is the total space occupied by the octagon.

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