Regular Polygon Calculator
Solve for the properties of any regular polygon. Enter the number of sides and the length of a single side to find the area, perimeter, and more.
Area = (n × s²) / (4 × tan(π/n))
Regular Hexagon (n=6) with side 10: Area = (6 * 100) / (4 * tan(30°)) ≈ 259.81
What is a regular polygon?
A regular polygon is a two-dimensional shape where all sides have the same length and all interior angles are equal. Examples include equilateral triangles, squares, and regular hexagons.
How do I calculate the area of a regular polygon?
The area can be calculated using the number of sides (n) and the side length (s) with the formula: Area = (n × s²) / (4 × tan(π/n)).
What is the apothem?
The apothem is the distance from the center of a regular polygon to the midpoint of one of its sides. It is used in an alternative area formula: Area = (Perimeter × Apothem) / 2.
Can I find the interior angle?
Yes! The interior angle of a regular polygon with n sides is calculated as: ((n - 2) × 180°) / n.
🔗 Related Calculators
📐 Formula
Area = (n × s²) / (4 × tan(π/n))
📝 Example Calculation
Regular Hexagon (n=6) with side 10: Area = (6 * 100) / (4 * tan(30°)) ≈ 259.81
❓ Frequently Asked Questions
What is a regular polygon?▼
A regular polygon is a two-dimensional shape where all sides have the same length and all interior angles are equal. Examples include equilateral triangles, squares, and regular hexagons.
How do I calculate the area of a regular polygon?▼
The area can be calculated using the number of sides (n) and the side length (s) with the formula: Area = (n × s²) / (4 × tan(π/n)).
What is the apothem?▼
The apothem is the distance from the center of a regular polygon to the midpoint of one of its sides. It is used in an alternative area formula: Area = (Perimeter × Apothem) / 2.
Can I find the interior angle?▼
Yes! The interior angle of a regular polygon with n sides is calculated as: ((n - 2) × 180°) / n.