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 regular 11-sided polygon. It represents one of the possible diagonal lengths in a hendecagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d_3 \) — Diagonal across three sides of hendecagon (m)
• \( r_i \) — Inradius of hendecagon (m)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

3. Formula Explanation

Mathematical Basis: This formula derives from trigonometric relationships in a regular hendecagon. The tangent function relates the inradius to the side length, while the sine functions account for the angular relationships between vertices separated by three sides in an 11-sided polygon.

Constants Used: π (Archimedes' constant) ≈ 3.141592653589793

Functions Used:

• sin() - Sine trigonometric function
• tan() - Tangent trigonometric function

4. Using the Calculator

Instructions: Enter the inradius value in meters. The inradius must be a positive number greater than zero. The calculator will compute the diagonal length across three sides of the regular hendecagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. When regular, all sides and angles are equal.

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

Q3: What is the inradius of a polygon?
A: The inradius is the radius of the circle inscribed within the polygon that touches all its sides.

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: What are practical applications of this calculation?
A: This calculation is useful in geometry, architectural design, and any field requiring precise measurements of regular polygons.