1. What is Diagonal across Three Sides of Hendecagon?

A diagonal across three sides of a hendecagon is a straight line joining two non-adjacent vertices that spans across three sides of the eleven-sided polygon. It represents one of the possible diagonal measurements in a regular hendecagon.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

Where:

• \( S \) — Side length of the hendecagon
• \( \pi \) — Mathematical constant pi (approximately 3.14159)
• \( \sin \) — Trigonometric sine function

Explanation: The formula utilizes trigonometric relationships in a regular hendecagon to calculate the length of diagonals that span across three sides.

3. Importance of Diagonal Calculation

Details: Calculating diagonals in regular polygons is important for geometric analysis, architectural design, and understanding the spatial properties of polygonal shapes. In a hendecagon, different diagonals have specific mathematical relationships with the side length.

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 diagonal length across three sides.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is an eleven-sided polygon. When regular, all sides and angles are equal.

Q2: How many diagonals does a hendecagon have?
A: A hendecagon has 44 diagonals in total, with different lengths depending on how many sides they span.

Q3: What are the practical applications of this calculation?
A: This calculation is used in geometry, architectural design, engineering, and any field requiring precise measurements of polygonal structures.

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: How accurate is the calculation?
A: The calculation is mathematically precise for regular hendecagons, using exact trigonometric relationships.