1. What is Perimeter of Nonagon given Inradius?

The perimeter of a nonagon (9-sided polygon) given its inradius is calculated using a specific geometric formula that relates the inradius to the perimeter through trigonometric functions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

3. Formula Explanation

Constants Used: pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used: tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Variables Used:

• Perimeter of Nonagon - Total distance around the edge of the Nonagon (m)
• Inradius of Nonagon - Radius of the circle inscribed inside the Nonagon (m)

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be greater than 0.

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: What is inradius?
A: Inradius is the radius of the circle that fits perfectly inside the polygon, touching all sides.

Q3: Why use this specific formula?
A: This formula provides an accurate mathematical relationship between the inradius and perimeter of a regular nonagon.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q5: What units should I use?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit system.