1. What is a Dodecagon?

A dodecagon is a 12-sided polygon with 12 angles. In a regular dodecagon, all sides are equal in length and all angles are equal in measure (150° each).

2. How Does the Calculator Work?

The calculator uses the dodecagon side length formula:

Where:

• \( r \) — Radius (distance from center to vertex)
• \( \pi/12 \) — 15° in radians (360° divided by 24)

Explanation: The formula calculates the length of each side of a regular dodecagon based on its circumradius (distance from center to any vertex).

3. Importance of Dodecagon Calculations

Details: Accurate dodecagon calculations are important in architecture, engineering, and design where twelve-sided shapes are used, such as in certain building layouts, clock faces, and decorative patterns.

4. Using the Calculator

Tips: Enter the radius (distance from center to any vertex) in any length units. The calculator will return the side length in the same units.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radius and apothem?
A: Radius is the distance from center to vertex, while apothem is the distance from center to midpoint of a side.

Q2: How do I calculate the perimeter?
A: Multiply the side length by 12 (number of sides).

Q3: What's the interior angle of a dodecagon?
A: Each interior angle is 150° in a regular dodecagon.

Q4: Can I calculate the area with this?
A: Not directly, but area = 3 × side² × (2 + √3) or 3 × radius².

Q5: What are real-world applications?
A: Used in architecture (buildings, windows), design (coins, medals), and engineering (bolts, gears).