1. What is the Inradius of Hendecagon?

The Inradius of Hendecagon is defined as the radius of the circle which is inscribed inside the Hendecagon. 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 formula:

Where:

• \( r_i \) — Inradius of Hendecagon (m)
• \( P \) — Perimeter of Hendecagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: This formula calculates the inradius of a regular Hendecagon (11-sided polygon) based on its perimeter using trigonometric relationships.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which is useful in various geometric constructions and calculations involving regular polygons.

4. Using the Calculator

Tips: Enter the perimeter 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 this formula?
A: The tangent function relates the central angle of the polygon to the ratio between the inradius and half the side length, which is fundamental in polygon geometry.

Q3: Can this formula 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 calculating inradius?
A: Inradius calculations are used in architecture, engineering design, and various geometric problems involving inscribed circles.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular Hendecagons, though computational precision may introduce minor rounding errors.