1. What is the Inradius of Hendecagon given Circumradius?

The inradius of a hendecagon is the radius of the circle inscribed inside the hendecagon that is tangent to all its sides. This calculator computes the inradius when the circumradius (radius of the circle passing through all vertices) is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• Circumradius of Hendecagon — Radius of the circumscribed circle (m)
• sin — Sine trigonometric function
• tan — Tangent trigonometric function

Explanation: This formula derives from the geometric properties of a regular hendecagon, relating the inradius to the circumradius through trigonometric functions of π/11.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various practical applications such as construction, design, and understanding the spatial properties of regular polygons.

4. Using the Calculator

Tips: Enter the circumradius of the hendecagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching all sides), while the circumradius is the radius of the circumscribed circle (passing through all vertices).

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

Q4: What are the practical applications of this calculation?
A: This calculation is useful in architecture, engineering design, and mathematical problems involving regular polygons.

Q5: How accurate is the calculation?
A: The calculation uses precise trigonometric functions and provides results accurate to 12 decimal places.