1. What is the Inradius of Dodecagon?

The inradius of a dodecagon is defined as the radius of the circle which is inscribed inside the dodecagon, touching all its sides. It represents the distance from the center of the dodecagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the inradius formula:

Where:

• \( r_i \) — Inradius of Dodecagon (m)
• \( S \) — Side length of Dodecagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula calculates the radius of the inscribed circle based on the side length of the regular dodecagon, incorporating the mathematical constant √3.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the largest circle that can fit inside a dodecagon, which has applications in various fields including engineering, architecture, and design.

4. Using the Calculator

Tips: Enter the side length of the dodecagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecagon?
A: A dodecagon is a polygon with twelve sides and twelve angles. A regular dodecagon has all sides equal and all interior angles equal.

Q2: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching the sides), while the circumradius is the radius of the circumscribed circle (passing through the vertices).

Q3: Can this formula be used for irregular dodecagons?
A: No, this formula is specifically for regular dodecagons where all sides are equal. Irregular dodecagons require different calculation methods.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering for gear design, and in various geometric pattern designs.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact for regular dodecagons, though the displayed result may be rounded for practical purposes.