Dodecagon Area Calculator
Calculate the area of a regular dodecagon from side length, perimeter, circumradius, or inradius
Calculate Dodecagon Area
Length of one side of the dodecagon
Dodecagon Area Result
Area Formula
Exact: A = 3 × (2 + √3) × a² = 11.196152 × a²
Approximate: A ≈ 11.19615242 × a²
Trigonometric: A = 3 × a² / tan(15°)
Example Calculations
Example 1: Side Length = 10 cm
Given: Side length (a) = 10 cm
Formula: A = 3 × (2 + √3) × a²
Calculation: A = 11.19615242 × 10² = 1119.615242 cm²
Result: Area ≈ 1119.6 cm²
Example 2: Side Length = 1 cm
Given: Side length (a) = 1 cm
Formula: A = 3 × (2 + √3) × a²
Calculation: A = 11.19615242 × 1² = 11.19615242 cm²
Result: Area ≈ 11.196 cm²
Area Formulas
From Side Length
A = 3(2 + √3) × a²
A ≈ 11.196 × a²
From Perimeter
A = P² × 3(2 + √3) / 144
From Circumradius
A = 3 × R² × sin(30°)
From Inradius
A = 12 × r² × tan(15°)
Angle Properties
Dodecagon Facts
A dodecagon has 12 sides and 12 vertices
Regular dodecagons have all equal sides and angles
The area coefficient 11.196 is exact: 3(2 + √3)
Dodecagons can be constructed with compass and straightedge
Understanding Dodecagon Area Calculation
Area Formula Derivation
The area of a regular dodecagon can be calculated using the general polygon formula: A = ½ × n × a × r, where n is the number of sides, a is the side length, and r is the apothem.
Simplified Formula
A = 3 × (2 + √3) × a²
A ≈ 11.19615242 × a²
This formula comes from substituting the apothem relationship for a 12-sided polygon and simplifying the trigonometric expressions.
Applications
- •Architecture and building design
- •Garden and landscape planning
- •Engineering calculations
- •Art and design projects
- •Mathematical education
Note: The exact coefficient 3(2 + √3) ensures precise calculations for all mathematical and engineering applications.