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Decagon Area Calculator

Introduction

Welcome to our Decagon Area Calculator! which will help you calculate the Decagon’s area quickly and accurately. A ten-sided closed polygon is called a decagon. So, the decagon has ten sides, ten interior angles, and ten vertices.

The interior angles of a decagon must be equal to 1440 degrees, and the exterior angles of a decagon must be equal to 360 degrees.

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

How to use the Decagon Area Calculator?

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

The variables in the Decagon Area Calculator include:

Side (s): Length of a side of a Regular Decagon.

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

A=5×s22×5+25A = \normalsize \dfrac{5\times s^2}{2} \times \sqrt{5+2\sqrt{5}}

Where,

s = Length of the side of the Decagon

What is a Decagon?

A decagon is a two-dimensional closed figure with ten sides. The decagon also has ten interior angles and ten vertices.

The sum of the interior angles of a decagon adds up to 1440 degrees, and the exterior angles add up to 360 degrees.

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

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

Properties of a Decagon

  1. A Decagon will have ten sides and ten angles.
  2. The interior angles of a Decagon will sum up to 1440 degrees.
  3. A Decagon has 35 diagonals.
  4. Each interior angle of a regular Decagon is equal to 144 degrees.

How is the Area of the Decagon Calculated?

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

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

A=5×s22×5+25A = \normalsize \dfrac{5\times s^2}{2} \times \sqrt{5+2\sqrt{5}}

Where,

s = Length of the side of the Decagon

Examples

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

We can calculate the area of the decagon using the following formula

A=5×s22×5+25=5×1022×5+25≈769.42  cm2\begin{aligned} A &= \normalsize \dfrac{5\times s^2}{2} \times \sqrt{5+2\sqrt{5}}\\[10pt] &= \normalsize \dfrac{5\times 10^2}{2} \times \sqrt{5+2\sqrt{5}}\\[10pt] &\approx 769.42 \; cm^2 \end{aligned}

As you can see, the area of the decagon with a side of length 10 cm is equivalent to 769.42 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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