1. What is the Inradius of Hendecagon?

The inradius of a hendecagon (11-sided polygon) is the radius of the circle that fits perfectly inside the hendecagon, touching all its sides. It represents the distance from the center of the hendecagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the inradius formula:

Where:

• \( r_i \) — Inradius of the hendecagon
• \( S \) — Side length of the hendecagon
• \( \pi \) — Mathematical constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the radius of the inscribed circle based on the side length of the regular hendecagon and its internal angles.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the largest circle that can fit inside a hendecagon, which has applications in design, architecture, and various engineering fields.

4. Using the Calculator

Tips: Enter the side length of the hendecagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. When all sides and angles are equal, it's called a regular hendecagon.

Q2: Why is the tangent function used in the formula?
A: The tangent function relates the side length to the inradius through the half-angle of the hendecagon's central angle.

Q3: Can this calculator be used for irregular hendecagons?
A: No, this formula only applies to regular hendecagons where all sides and angles are equal.

Q4: What are practical applications of inradius calculation?
A: Inradius calculations are used in manufacturing, architecture, and design where circular components need to fit within polygonal shapes.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact for regular hendecagons, though practical measurements may have slight variations.