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's an important geometric property that helps in various mathematical and engineering calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• Diagonal Across Three Sides — The straight line joining two non-adjacent vertices across three sides of the dodecagon

Explanation: This formula establishes the mathematical relationship between the inradius of a regular dodecagon and the diagonal that spans three of its sides.

3. Importance of Inradius Calculation

Details: Calculating the inradius is crucial for geometric analysis, architectural design, and various engineering applications where precise measurements of regular polygons are required.

4. Using the Calculator

Tips: Enter the diagonal across three sides measurement in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular dodecagon?
A: A regular dodecagon is a polygon with 12 equal sides and 12 equal angles, making it a perfectly symmetrical shape.

Q2: How is diagonal across three sides measured?
A: It's the straight line distance between two non-adjacent vertices that have exactly two vertices between them along the perimeter.

Q3: Can this formula be used for irregular dodecagons?
A: No, this formula specifically 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 architecture, mechanical engineering, and geometric design where dodecagonal shapes are employed.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular dodecagons, with accuracy depending on the precision of the input measurement.