1. What is Inradius of Nonagon?

The inradius of a nonagon is the radius of the circle that fits perfectly inside the nonagon, touching all nine sides. It represents the distance from the center of the nonagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the inradius formula:

Where:

• \( r_i \) — Inradius of the nonagon
• \( A \) — Area of the nonagon
• \( \pi \) — Mathematical constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the inradius by relating the area of the nonagon to its geometric properties using trigonometric functions.

3. Importance of Inradius Calculation

Details: The inradius is important in geometry for determining the size of the inscribed circle, calculating other geometric properties, and solving various geometric problems involving nonagons.

4. Using the Calculator

Tips: Enter the area of the nonagon in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a nonagon?
A: A nonagon is a nine-sided polygon with nine angles and nine vertices.

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

Q3: Can this formula be used for other polygons?
A: No, this specific formula applies only to nonagons. Other polygons have different formulas for calculating inradius.

Q4: What units should I use for area?
A: The calculator uses square meters, but you can use any consistent area unit as long as the inradius will be in the corresponding length unit.

Q5: Is the nonagon assumed to be regular?
A: Yes, this formula applies only to regular nonagons where all sides and angles are equal.