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

The formula calculates the circumradius of a regular hendecagon (11-sided polygon) when its inradius is known. The circumradius is the radius of the circle that passes through all vertices of the hendecagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function
• \( \sin \) — Sine trigonometric function
• Inradius — Radius of the inscribed circle

Explanation: This formula derives from the geometric properties of regular polygons, specifically the relationship between the circumradius and inradius of a regular hendecagon.

3. Importance of Circumradius Calculation

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

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hendecagon?
A: A regular hendecagon is an 11-sided polygon with all sides equal and all interior angles equal (approximately 147.27 degrees each).

Q2: What's the difference between circumradius and inradius?
A: The circumradius is the radius of the circle passing through all vertices, while the inradius is the radius of the circle inscribed within the polygon.

Q3: Can this formula be used for other polygons?
A: No, this specific formula applies only to regular hendecagons. Other regular polygons have different trigonometric relationships.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric pattern creation involving 11-sided figures.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise, using the exact trigonometric relationships for a regular hendecagon.