1. What is 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 formula:

Where:

• \( r_i \) — Inradius of Dodecagon (m)
• \( d_5 \) — Diagonal Across Five Sides of Dodecagon (m)

Explanation: The inradius of a regular dodecagon is exactly half the length of the diagonal that spans across five sides of the polygon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various engineering applications where the properties of regular polygons need to be determined for design and construction purposes.

4. Using the Calculator

Tips: Enter the diagonal across five sides 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 equal sides and twelve equal angles.

Q2: How is the diagonal across five sides defined?
A: The diagonal across five sides is a straight line joining two non-adjacent vertices across five sides of the dodecagon.

Q3: Is this formula specific to regular dodecagons?
A: Yes, this formula applies only to regular dodecagons where all sides and angles are equal.

Q4: Can this calculator be used for other polygons?
A: No, this specific formula and calculator are designed specifically for regular dodecagons.

Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, engineering projects, and geometric pattern creation where dodecagonal shapes are used.