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 hendecagon (11-sided polygon).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Circumradius \) — Radius of the circumscribed circle that passes through all vertices of the hendecagon
• \( \pi \) — Mathematical constant approximately equal to 3.14159
• \( \sin \) — Trigonometric sine function

3. Formula Explanation

Details: The formula is derived from the geometric properties of regular polygons. For a regular hendecagon, the angle between consecutive vertices at the center is \( \frac{2\pi}{11} \). A diagonal spanning three sides corresponds to an angle of \( \frac{6\pi}{11} \) at the center, but the chord length formula uses half this angle in the sine function.

4. Using the Calculator

Tips: Enter the circumradius of the hendecagon in meters. The value must be positive and greater than zero. The calculator will compute the length of the diagonal that spans 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 vertices. When all sides and angles are equal, it's called a regular hendecagon.

Q2: How many diagonals does a hendecagon have?
A: A hendecagon has 44 diagonals in total, calculated using the formula \( \frac{n(n-3)}{2} \) where n = 11.

Q3: What is the circumradius of a polygon?
A: The circumradius is the radius of the circumscribed circle that passes through all vertices of the polygon.

Q4: Can this calculator be used for irregular hendecagons?
A: No, this calculator is specifically designed for regular hendecagons where all sides and angles are equal.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering design, and any field that involves regular polygon geometry.