1. What is the Height of Hendecagon?

The height of a hendecagon (11-sided polygon) is the perpendicular distance from one side to the opposite vertex. It represents the maximum vertical measurement of the regular hendecagon when oriented with one side horizontal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the height of a regular hendecagon based on its side length using trigonometric relationships derived from the polygon's internal angles.

3. Importance of Height Calculation

Details: Calculating the height of a hendecagon is essential in geometry, architecture, and engineering applications where regular 11-sided shapes are used. It helps in determining the overall dimensions and spatial requirements of hendecagonal structures.

4. Using the Calculator

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

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: 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° or π/22 radians).

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

Q4: What are practical applications of hendecagon height calculation?
A: This calculation is useful in architectural design, manufacturing of hendecagonal components, and geometric modeling.

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