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

The formula calculates the side length of a regular hendecagon (11-sided polygon) when its height is known. It uses trigonometric relationships to determine the side length based on the polygon's geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side of Hendecagon (m)
• \( h \) — Height of Hendecagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula derives from the geometric properties of a regular hendecagon, where the tangent function relates the height to the side length through the central angle of the polygon.

3. Importance of Side Calculation

Details: Calculating the side length of a hendecagon is essential in geometry, architecture, and design applications where regular polygons are used. It helps in determining the dimensions and proportions of hendecagonal structures.

4. Using the Calculator

Tips: Enter the height of the hendecagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding side length.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with eleven sides and eleven angles. When all sides and angles are equal, it is called a regular hendecagon.

Q2: Why is π/22 used in the formula?
A: π/22 represents half of the central angle of a hendecagon (360°/11 = 32.727°, half is 16.363° which equals π/22 radians).

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 hendecagon calculations?
A: Hendecagons are used in architectural design, coin design (some countries), and various decorative patterns and structures.

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