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

The formula calculates the side length of a regular hendecagon (11-sided polygon) when its circumradius is known. It's derived from trigonometric relationships in regular polygons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

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

3. Importance of Side Length Calculation

Details: Calculating the side length of a regular hendecagon is important in geometry, architecture, and design applications where precise measurements of 11-sided polygons are required.

4. Using the Calculator

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

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: What is circumradius?
A: Circumradius is the radius of a circle that passes through all the vertices of a polygon. For regular polygons, it's the distance from the center to any vertex.

Q3: Why is π/11 used in the formula?
A: π/11 represents half of the central angle of a regular hendecagon (360°/11 = 32.727°, which is approximately 0.5712 radians).

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

Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, engineering projects, and mathematical studies involving regular polygons.