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:
- is the area of a regular polygon;
- is the regular polygon's number of sides;
- is the length of the regular polygon's side;
- is the incircle radius or apothem of the regular polygon
Since we want to find the area of a decagon, we can replace with . Consequently, we can find the value of using and with the help of this equation:
That said, we can simplify the regular polygon's area formula by replacing with and with that function to have:
We can simplify it further to 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 . 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 ), circumcircle radius (R) (equal to ), or the apothem (r).
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How do I calculate decagon area?
To calculate the decagon area:
- Measure the side of the decagon. Let's say we get
- 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