1. What is Inradius of Nonagon?

The inradius of a nonagon is defined as the radius of the circle which is inscribed inside the nonagon. It is the distance from the center of the nonagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Nonagon (m)
• \( S \) — Side of Nonagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the radius of the inscribed circle based on the side length of the regular nonagon using trigonometric relationships.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various practical applications such as construction, design, and engineering where regular nonagonal shapes are used.

4. Using the Calculator

Tips: Enter the side length of the nonagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a nonagon?
A: A nonagon is a nine-sided polygon. A regular nonagon has all sides equal and all interior angles equal.

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

Q3: Can this formula be used for irregular nonagons?
A: No, this formula is specifically for regular nonagons 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 various geometric applications involving regular nonagonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular nonagons, though practical measurements may have some degree of error.