Dodecagon Calculator
Calculate all properties of a regular dodecagon: area, perimeter, diagonals, and more
Calculate Dodecagon Properties
Length of one side of the regular dodecagon
Dodecagon Properties
Diagonal Lengths
Example Calculation
Regular Dodecagon with 10 cm side
Given: Side length (a) = 10 cm
Perimeter: P = 12 × 10 = 120 cm
Area: A = 3 × (2 + √3) × 10² ≈ 11.196 × 100 ≈ 1119.6 cm²
Circumradius: R = ½ × 10 × (√6 + √2) ≈ 19.32 cm
Inradius: r = ½ × 10 × (2 + √3) ≈ 18.66 cm
Dodecagon Facts
A dodecagon has 12 sides and 12 vertices
Each interior angle measures 150°
Sum of all interior angles is 1800°
A regular dodecagon has 54 diagonals
The word "dodecagon" comes from Greek "dodeka" (twelve)
Key Formulas
Perimeter
P = 12 × a
Area
A = 3(2 + √3) × a²
Circumradius
R = ½a(√6 + √2)
Inradius
r = ½a(2 + √3)
Number of Diagonals
n(n-3)/2 = 54
Understanding Dodecagons
What is a Dodecagon?
A dodecagon is a polygon with twelve sides. The name comes from the Greek word "dodeka," meaning twelve. When all sides are equal and all angles are identical, it's called a regular dodecagon.
Properties
- •12 equal sides in a regular dodecagon
- •12 vertices and 12 interior angles
- •Each interior angle measures 150°
- •Each exterior angle measures 30°
Real-World Applications
- •Architecture and building design
- •Clock faces and time-related designs
- •Art and decorative patterns
- •Engineering and mechanical design
- •Game design and board layouts
Fun Fact: A regular dodecagon can be constructed with compass and straightedge, making it useful in geometric constructions.