1. What is the Side of Dodecagon given Width Formula?

The formula calculates the side length of a regular dodecagon (12-sided polygon) when the width (distance between parallel sides) is known. It provides a precise geometric relationship between these two measurements.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side length of the dodecagon (m)
• \( w \) — Width of the dodecagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the geometric properties of a regular dodecagon and the trigonometric relationships between its sides and width.

3. Importance of Side Calculation

Details: Calculating the side length from the width is essential in geometric design, architecture, and engineering applications involving dodecagonal shapes. It helps in material estimation and structural planning.

4. Using the Calculator

Tips: Enter the width of the dodecagon in meters. The value must be positive and valid. The calculator will compute the corresponding side length.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular dodecagon?
A: A regular dodecagon is a 12-sided polygon where all sides are equal in length and all interior angles are equal (150° each).

Q2: How accurate is this formula?
A: The formula is mathematically exact for regular dodecagons and provides precise results when accurate measurements are used.

Q3: Can this formula be used for irregular dodecagons?
A: No, this formula only applies to regular dodecagons where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, jewelry making, and any field requiring precise dodecagonal geometry.

Q5: How is the width defined for a dodecagon?
A: The width is the horizontal distance between two parallel sides of the regular dodecagon, measured perpendicular to those sides.