Just enter the pentagon's side below and click Calculate Area. Use a dot or comma as the decimal separator.
Regular Pentagon Area Calculator
Answer:
How to use the calculator
- Enter the Side length of the regular pentagon.
- Select the unit of measurement.
- Click Calculate Area to see the result.
Regular Pentagon Area Formula
The area of a regular pentagon is calculated from side L:
A = (L² × √(25 + 10√5)) ÷ 4 ≈ 1.720 × L²
A regular pentagon has 5 equal sides and interior angles of 108°. It can be divided into 5 isosceles triangles of equal area, whose calculation leads to the expression with radicals above.
Practical Examples
| Side (L) | Area (A ≈ 1.720 × L²) |
|---|---|
| 1 m | 1.720 m² |
| 6 cm | 61.937 cm² |
| 10 m | 172.048 m² |
| 4 mm | 27.528 mm² |
| 2.5 cm | 10.753 cm² |
Frequently Asked Questions
What is the formula for the area of a regular pentagon?
The area is A = (L² × √(25 + 10√5)) / 4 ≈ 1.720 × L². For example, side 6 cm: A ≈ 1.720 × 36 ≈ 61.94 cm².
What is the apothem of a regular pentagon?
The apothem is the distance from the centre to the midpoint of a side: a = L / (2 × tan(36°)) ≈ 0.688 × L. The area can also be written as A = (5 × L × a) / 2.
Why does the formula contain √(25 + 10√5)?
This expression comes from the exact calculation using trigonometry. The apothem involves tan(36°) = √(5 − 2√5), and simplifying the total area of the 5 interior triangles leads to the radical √(25 + 10√5).
Can I use a comma instead of a decimal point?
Yes. This calculator accepts both a comma and a period as the decimal separator.
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