1. What is Diagonal across Five Sides of Hendecagon?

Diagonal across Five Sides of Hendecagon is a straight line joining two non-adjacent sides across five sides of the Hendecagon. It's an important geometric measurement in an 11-sided polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d5 \) — Diagonal across Five Sides of Hendecagon (m)
• \( r_i \) — Inradius of Hendecagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

3. Formula Explanation

Mathematical Functions:

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

The formula combines trigonometric relationships to calculate the diagonal measurement based on the inradius of the hendecagon.

4. Using the Calculator

Instructions: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the diagonal across five sides of the hendecagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hendecagon?
A: A hendecagon is an 11-sided polygon, also known as an undecagon.

Q2: What is the Inradius of a polygon?
A: The inradius is the radius of the circle that fits perfectly inside the polygon, touching all its sides.

Q3: Why are trigonometric functions used in this calculation?
A: Trigonometric functions help relate the inradius to various diagonal measurements through the angles of the regular polygon.

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, architecture, engineering, and any field dealing with regular polygonal structures.