1. What is Inradius of Dodecagon?

The inradius of a dodecagon is the radius of the circle that fits perfectly 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 formula:

Where:

• \( r_i \) — Inradius of Dodecagon (m)
• \( r_c \) — Circumradius of Dodecagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• \( \sqrt{6} \) — Square root of 6 (approximately 2.449)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the inradius of a regular dodecagon based on its circumradius, using geometric relationships between the two radii.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and engineering applications where the internal dimensions of a dodecagon need to be determined for design, construction, or analysis purposes.

4. Using the Calculator

Tips: Enter the circumradius of the dodecagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding inradius.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between inradius and circumradius?
A: The inradius is always smaller than the circumradius for any regular polygon, including a dodecagon.

Q2: Can this formula be used for irregular dodecagons?
A: No, this formula is specifically for regular dodecagons where all sides and angles are equal.

Q3: What are practical applications of this calculation?
A: This calculation is useful in architectural design, engineering projects, and geometric analysis involving dodecagonal shapes.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecagons, though practical measurements may have some degree of error.

Q5: Can I calculate circumradius from inradius using this formula?
A: Yes, the formula can be rearranged to solve for circumradius given the inradius value.