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.

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:

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).

Finding this tool interesting? Here are some of our other polygon tools that you might find interesting too:

• Polygon calculator
• Dodecagon area calculator
• Dodecagon calculator
• Heptagon area calculator
• Heptagon calculator
• Decagon calculator
• Polygon angle calculator

To calculate the decagon area:

1. Measure the side of the decagon. Let's say we get 2 inches.
2. Square the side of the decagon. 2 inches × 2 inches = 4 in².
3. Multiply the squared side by 2.5/tan(18°) or 7.694208843 to have: 4 in² × 7.694208843 = 30.77683537 in² ≈ 30.777 in².

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