1. What is the Inradius of Nonagon?

The Inradius of 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:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function
• Perimeter of Nonagon — Total distance around the edge of the Nonagon

Explanation: This formula calculates the inradius of a regular nonagon based on its perimeter using trigonometric relationships.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle within a nonagon, which has applications in various fields including architecture, engineering, and design.

4. Using the Calculator

Tips: Enter the perimeter 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 polygon with nine sides and nine angles. A regular nonagon has all sides and angles equal.

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 nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.

Q4: What are practical applications of inradius calculation?
A: Inradius calculations are used in construction, manufacturing, and design where precise geometric measurements are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular nonagons, though real-world measurements may have practical limitations.