1. What is the Inradius of Dodecagon given Width?

The inradius of a dodecagon is defined as the radius of the circle which is inscribed inside the dodecagon. When given the width of a regular dodecagon, the inradius can be calculated using a simple mathematical relationship.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Dodecagon (m)
• \( w \) — Width of Dodecagon (m)

Explanation: The inradius of a regular dodecagon is exactly half of its width measurement. This relationship holds true for all regular dodecagons.

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 analysis purposes.

4. Using the Calculator

Tips: Enter the width of the dodecagon in meters. The value must be a positive number 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. When all sides and angles are equal, it is called a regular dodecagon.

Q2: How is width defined for a dodecagon?
A: The width of a dodecagon is the horizontal distance from the leftmost edge to the rightmost edge of the regular dodecagon.

Q3: Does this formula work 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 useful in architecture, engineering design, and various geometric problems involving regular dodecagons.

Q5: Can I use different units of measurement?
A: Yes, as long as you maintain consistency. The calculator uses meters, but the formula works with any unit of length.