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, touching all its 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 formula:

Where:

• \( r_i \) — Inradius of Nonagon (m)
• \( h \) — Height of Nonagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sec \) — Secant trigonometric function

3. Formula Explanation

Details: This formula derives from the geometric properties of a regular nonagon. The secant function accounts for the angular relationships between the height and the inradius in a 9-sided polygon.

4. Using the Calculator

Tips: Enter the height of the nonagon in meters. The height must be a positive value greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular nonagon?
A: A regular nonagon is a nine-sided polygon where all sides are equal in length and all interior angles are equal (140° each).

Q2: How is height defined for a nonagon?
A: Height of a nonagon is the length of a perpendicular line drawn from one vertex to the opposite side.

Q3: What are typical values for nonagon inradius?
A: The inradius depends on the size of the nonagon. For a regular nonagon, the inradius is always smaller than the circumradius.

Q4: Can this formula be used for irregular nonagons?
A: No, this formula is specifically for regular nonagons where all sides and angles are equal.

Q5: What is the relationship between inradius and side length?
A: For a regular nonagon, the inradius can also be calculated from the side length using the formula: \( r_i = \frac{s}{2\tan(\pi/9)} \), where s is the side length.