1. What is Circumradius of Dodecagon?

The circumradius of a dodecagon is the radius of a circumcircle that touches all vertices of the regular dodecagon. It's an important geometric property that relates to the size and proportions of the 12-sided polygon.

2. How Does the Calculator Work?

The calculator uses the mathematical relationship between inradius and circumradius:

This formula calculates the circumradius based on the given inradius of a regular dodecagon.

3. Formula Explanation

Mathematical Components:

• \( \sqrt{6} \) — Square root of 6 (approximately 2.449)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.414)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• Inradius — The radius of the inscribed circle

The formula demonstrates the fixed geometric relationship between the inscribed and circumscribed circles of a regular dodecagon.

4. Using the Calculator

Instructions: Enter the inradius value in meters. The inradius must be a positive number. The calculator will compute the corresponding circumradius of the dodecagon.

5. Frequently Asked Questions (FAQ)

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

Q2: How is inradius different from circumradius?
A: Inradius is the radius of the circle inscribed inside the polygon (touching all sides), while circumradius is the radius of the circle that passes through all vertices.

Q3: Can this calculator 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 useful in geometry, architecture, engineering design, and any field working with regular polygonal shapes.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact for regular dodecagons, though numerical precision depends on the implementation.