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Octagon Area Calculator

Introduction

Welcome to our Octagon Area Calculator! which will help you calculate the octagon’s area quickly and accurately. An Octagon is basically a two-dimensional closed shape with eight sides and eight angles. If all the sides of an Octagon are equal, it is called a regular Octagon. Whereas, if the sides of the Octagon are not equal, it is called an irregular Octagon.

The space occupied by the Octagon in a two-dimensional plane is called the Octagon’s area.

How to use the Octagon Area Calculator?

Using the Octagon Area calculator, you can calculate the area of the Octagon by inputting the length of the side of the Octagon.

The variables in the Octagon Area Calculator include:

Side (a): Length of a side of a Regular Octagon.

Area of Regular Octagon (A) The area of the Regular Octagon is calculated using the following formula.

A=2(1+2)×a2A = 2(1 + \sqrt{2}) \times a^2

Where,

a = Length of the side of the Octagon

What is an Octagon?

An Octagon is an eight-sided polygon. It is a closed two-dimensional figure. It consists of eight interior angles and eight exterior angles.

The sum of all the interior angles will equal 1080 degrees, and the sum of all exterior angles will equal 360 degrees.

Basically, Octagons can be classified into four types based on the length of their sides, a measure of their angles, and their vertices.

  1. Regular Octagon: if all eight sides of the Octagon are equal and all eight angles are equal, then the Octagon is called a regular Octagon.

  2. Irregular Octagon: if the sides and the angles of the Octagon are not equal, then it is called an Irregular Octagon.

  3. Convex Octagon: if all of the vertices of the Octagon point outward, then it is called a Convex Octagon.

  4. Concave Octagon: if at least one of the Octagon’s vertex points inward, it is called a Concave Octagon.

Properties of an Octagon

  1. An Octagon will have eight sides and eight angles.

  2. The interior angles of an Octagon will sum up to 1080 degrees.

  3. An Octagon has 20 diagonals.

How is the Area of the Octagon Calculated?

The total space taken up by the Octagon on a two-dimensional plane is called the area of the Octagon. It could also be considered as the number of square units required to fill the region inside the Octagon. Hence, the measurement will be in square units.

We can calculate the area of the Octagon using the following formula.

A=2(1+2)×a2A = 2(1 + \sqrt{2}) \times a^2

Where,

A = Area of the Regular Octagon

a = Length of the side of the Octagon

Examples

Let’s say there is a regular Octagon with a length of side equal to 8 cm. What will be the area of the Octagon?

The area of the Octagon can be calculated using the following formula.

A=2(1+2)×a2=2(1+2)×82=309.02  cm2\begin{aligned} A &= 2(1 + \sqrt{2}) \times a^2 \\[10pt] &= 2 (1+\sqrt{2}) \times 8^2 \\[10pt] &= 309.02 \; cm^2 \end{aligned}

As shown above, in the example, the area of the Octagon is 309.02 sq cm.

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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