Area of a Regular Polygon Calculator
Calculate area, perimeter, and properties of regular polygons using various input methods
Calculate Regular Polygon Area
Minimum 3 sides. Hexagon
Choose the known parameter
Length of each side of the regular polygon
Example Calculation
Regular Hexagon Example
Number of sides: 6 (hexagon)
Side length: 5 units
Formula: A = n × a² × cot(π/n) / 4
Step-by-Step Calculation
A = 6 × 5² × cot(π/6) / 4
A = 6 × 25 × cot(30°) / 4
A = 6 × 25 × √3 / 4
A = 150 × 1.732 / 4
A ≈ 64.95 square units
Common Regular Polygons
Polygon Facts
All sides and angles are equal in regular polygons
Apothem is the distance from center to side midpoint
Circumradius connects center to vertices
Interior angles sum: (n-2) × 180°
Exterior angles always sum to 360°
Understanding Regular Polygon Area Calculation
What is a Regular Polygon?
A regular polygon is a polygon with all sides equal in length and all interior angles equal. These symmetrical shapes have many practical applications in architecture, engineering, and design.
Key Properties
- •Side Length (a): Length of each side
- •Apothem: Distance from center to side midpoint
- •Circumradius: Distance from center to vertex
- •Perimeter: Sum of all side lengths
Area Formulas
Using Side Length:
A = n × a² × cot(π/n) / 4
Using Apothem:
A = n × ap² × tan(π/n)
Using Circumradius:
A = n × R² × sin(2π/n) / 2
Using Perimeter:
A = perimeter × apothem / 2
Angle Relationships
- •Interior Angle: (n-2) × 180° / n
- •Exterior Angle: 360° / n
- •Central Angle: 360° / n
Applications
- •Architecture and construction planning
- •Land surveying and area measurement
- •Engineering design and manufacturing
- •Art and graphic design