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Nonagon Area Calculator

Introduction

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

The space occupied by the Nonagon in a two-dimensional plane is called the area of the Nonagon.

How to use the Nonagon Area Calculator?

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

The variables in the Nonagon Area Calculator include:

Side (a)
Length of a side of a Regular Nonagon.

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

A=9×a24×cot(1809)A = \normalsize \dfrac{9\times a^2}{4} \times \text{cot}(\dfrac{180}{9})

Where,

a = Length of the side of Nonagon

What is a Nonagon?

A Nonagon is a nine-sided polygon. It is a closed two-dimensional figure with nine interior and nine exterior angles.

The sum of all the interior angles will equal 1260 degrees, and the sum of all exterior angles will equal 360 degrees.

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

  1. Regular Nonagon: if all nine sides of the Nonagon are equal and all nine angles are equal, then the Nonagon is called a regular Nonagon.
  2. Irregular Nonagon: if the sides and the angles of the Nonagon are not equal, then it is called an Irregular Nonagon.
  3. Convex Nonagon: if all of the vertices of the Nonagon point outward, then it is called a Convex Nonagon.
  4. Concave Nonagon: if at least one of the Nonagon’s vertex points inward, it is called a Concave Nonagon.

Properties of a Nonagon

  1. A Nonagon will have nine sides and nine angles.
  2. The interior angles of a Nonagon will sum up to 1260 degrees.
  3. A Nonagon has 27 diagonals.
  4. Each interior angle of a regular Nonagon is equal to 140 degrees.

How is the Area of the Nonagon Calculated?

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

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

A=9×a24×cot(1809)A = \normalsize \dfrac{9\times a^2}{4} \times \text{cot}(\dfrac{180}{9})

Where,

A = Area of the Regular Nonagon

a = Length of the side of the Nonagon

Examples

Let’s say there is a regular nonagon with a length of side equal to 10 cm. What is the area of the nonagon?

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

A=9×a24×cot(1809)=9×1024×cot(1809)≈618.18  cm2\begin{aligned} A &= \normalsize \dfrac{9\times a^2}{4} \times \text{cot}(\dfrac{180}{9}) \\[10pt] &= \normalsize \dfrac{9\times 10^2}{4} \times \text{cot}(\dfrac{180}{9}) \\[10pt] &\approx 618.18 \; cm^2 \end{aligned}

As shown above, in the calculation, the area of the nonagon is equal to 618.18 square 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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