1. What is the Circumradius of Hendecagon?

The circumradius of a hendecagon (11-sided polygon) is the radius of a circle that passes through all vertices of the hendecagon. It represents the distance from the center of the hendecagon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Hendecagon (m)
• \( S \) — Side of Hendecagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function

Explanation: The formula calculates the circumradius based on the side length and the sine of the central angle (π/11 radians) of the hendecagon.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, architecture, and engineering for designing and analyzing regular hendecagonal structures and patterns.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. It is also known as an undecagon.

Q2: How is this formula derived?
A: The formula is derived from the relationship between the side length and the central angle in a regular polygon, using trigonometric functions.

Q3: Can this calculator be used for irregular hendecagons?
A: No, this calculator is specifically designed for regular hendecagons where all sides and angles are equal.

Q4: What are practical applications of hendecagon calculations?
A: Hendecagons are used in architectural design, coin design, and various geometric patterns in art and engineering.

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