# Decagon Area Calculator

This decagon area calculator will help you quickly determine the area of a regular decagon. A decagon is a regular polygon with 10 sides. These 10 sides are equal in measurement and comprise the perimeter of the decagon. Like any polygon, a decagon has an enclosed space or area that we can calculate using geometry and trigonometry.

Keep on reading to discover:

- How to find the area of a decagon;
- How to use this decagon area calculator; and
- Some frequently asked questions about decagon.

## How to find the area of a decagon

To find the area of a decagon, we can use the area formula of any regular polygon, as shown below:

Where:

- $A$ is the area of a regular polygon;
- $n$ is the regular polygon's number of sides;
- $a$ is the length of the regular polygon's side;
- $r$ is the incircle radius or apothem of the regular polygon

Since we want to find the area of a decagon, we can replace $n$ with $10$. Consequently, we can find the value of $r$ using $a$ and $n$ with the help of this equation:

That said, we can simplify the regular polygon's area formula by replacing $n$ with $10$ and $r$ with that function to have:

We can simplify it further to $A_\text{decagon} = 7.694208843\times a^2$ but isn't it nice to know how we derived this area of a regular decagon formula? 🙂

Now, let's say we have a decagon with a side that measures $5\ \text{cm}$. Using our decagon area formula, we get:

## How to use this calculator

This tool is very straightforward. To find the area of a regular decagon, all you have to do is:

**Enter the measurement of side (a)**; or**Input other measurements of your decagon**like its**perimeter**(which is only $10\times a$),**circumcircle radius (R)**(equal to $\frac{a}{2\times \sin(18\degree)}$), or the**apothem (r)**.

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## FAQ

### How do I calculate decagon area?

To calculate the decagon area:

**Measure the side of the decagon**. Let's say we get`2 inches`

.**Square the side of the decagon**.`2 inches × 2 inches = 4 in²`

.**Multiply the squared side by 2.5/tan(18°)**or**7.694208843**to have:`4 in² × 7.694208843 = 30.77683537 in²`

.`≈ 30.777 in²`

### What is the area of a decagon with a side of 3 cm?

The area of a 3-cm-sided decagon is **approximately 69.25 cm²**. We get that value by substituting 3 cm as the value of `a`

in this formula:

`decagon area = 7.694208843 × a²`

.

Substituting 3 cm, we get:

`decagon area = 7.694208843 × (3 cm)²`

`= 7.694208843 × 9 cm²`

`= 69.24787959 cm²`

`≈ 69.25 cm²`