1. What is Circumradius of Hendecagon?

The circumradius of a hendecagon (11-sided polygon) is the radius of a circumcircle that touches all vertices of the hendecagon. It's an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Hendecagon (m)
• \( h \) — Height of Hendecagon (m)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

3. Formula Explanation

Details: This formula derives from trigonometric relationships in a regular hendecagon. The height (h) is related to the circumradius through tangent and sine functions of angles determined by the polygon's geometry.

4. Using the Calculator

Tips: Enter the height of the hendecagon in meters. The value must be positive. The calculator will compute the corresponding circumradius.

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: How is height defined for a hendecagon?
A: The height of a hendecagon is the length of a perpendicular line drawn from one vertex to the opposite side.

Q3: What are practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering design, and any field working with regular polygons.

Q4: Can this formula be used for irregular hendecagons?
A: No, this formula applies only to regular hendecagons where all sides and angles are equal.

Q5: What is the relationship between circumradius and side length?
A: For a regular hendecagon, the circumradius (R) and side length (s) are related by: \( s = 2R \cdot \sin(\pi/11) \).