Dodecagon Side Length Calculator

Dodecagon Side Length Formula:

\[ \text{side} = 2 \times r \times \sin\left(\frac{\pi}{12}\right) \]

Side Length:

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1. What is a Dodecagon?

A dodecagon is a 12-sided polygon. When it's regular (all sides and angles equal), the side length can be calculated from the radius (distance from center to vertex) using trigonometric functions.

2. How Does the Calculator Work?

The calculator uses the dodecagon side length formula:

\[ \text{side} = 2 \times r \times \sin\left(\frac{\pi}{12}\right) \]

Where:

\( r \) — Radius (distance from center to vertex)
\( \pi \) — Mathematical constant (~3.14159)
\( \sin \) — Trigonometric sine function

Explanation: The formula calculates the length of one side of a regular dodecagon based on its radius using trigonometric relationships.

3. Importance of Side Length Calculation

Details: Knowing the side length is essential for construction, design, and geometric calculations involving dodecagons. It's used in architecture, engineering, and various design fields.

4. Using the Calculator

Tips: Enter the radius in any units (the result will be in the same units). The radius must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: What's the exact value of sin(π/12)?
A: sin(π/12) equals (√6 - √2)/4 ≈ 0.2588

Q2: Can I calculate radius from side length?
A: Yes, by rearranging the formula: r = side / (2 × sin(π/12))

Q3: What's the difference between radius and apothem?
A: Radius is center-to-vertex distance, apothem is center-to-side distance. For dodecagon, apothem = r × cos(π/12)

Q4: How many degrees in each dodecagon angle?
A: Interior angles are 150° each in a regular dodecagon.

Q5: What are real-world applications of dodecagons?
A: Used in architecture (buildings, windows), design (coins, patterns), and engineering (structural components).