1. What is the Height of Hendecagon given Circumradius?

The height of a hendecagon (11-sided polygon) given its circumradius is the perpendicular distance from one vertex to the opposite side. This calculation is important in geometry and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Circumradius \) — The radius of the circumscribed circle (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the height of a regular hendecagon based on its circumradius using trigonometric relationships between the central angles and side lengths.

3. Importance of Height Calculation

Details: Calculating the height of a hendecagon is crucial for architectural design, geometric analysis, and various engineering applications where regular polygons are used.

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. It is also known as an undecagon.

Q2: What is circumradius?
A: Circumradius is the radius of a circle that passes through all the vertices of a polygon.

Q3: Can this formula be used for irregular hendecagons?
A: No, this formula applies only to regular hendecagons where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric modeling where regular 11-sided shapes are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hendecagons, though practical measurements may have slight variations.