1. What is the Side of Hendecagon given Inradius Formula?

The formula calculates the side length of a regular hendecagon (11-sided polygon) when the inradius (radius of the inscribed circle) is known. This geometric relationship helps in determining polygon dimensions from its inscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The formula derives from the geometric relationship between the inscribed circle and the sides of a regular polygon, using trigonometric functions to calculate side length.

3. Importance of Side Length Calculation

Details: Calculating side length from inradius is essential in geometry, architecture, and engineering for designing and constructing regular polygons with specific inscribed circles.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hendecagon?
A: A regular hendecagon is an 11-sided polygon where all sides are equal in length and all interior angles are equal.

Q2: Why use the tangent function in this formula?
A: The tangent function relates the inradius to half the side length through the central angle of the polygon.

Q3: Can this formula be used for other polygons?
A: Similar formulas exist for other regular polygons, but the angle (π/n) changes based on the number of sides.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, manufacturing of polygonal components, and geometric modeling.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular hendecagon, though practical measurements may have slight variations.