1. What is the Inradius of N-gon?

The Inradius of N-gon is defined as the radius of the circle which is inscribed inside the N-gon. It represents the distance from the center of the polygon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the Inradius of N-gon formula:

Where:

• \( r_i \) — Inradius of N-gon (m)
• \( l_e \) — Edge Length of N-gon (m)
• \( N \) — Number of Sides of N-gon
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the radius of the inscribed circle based on the side length and number of sides of the regular polygon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the largest circle that can fit inside a regular polygon, which has applications in various fields including architecture, engineering, and design.

4. Using the Calculator

Tips: Enter the edge length in meters and the number of sides (must be at least 3). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular N-gon?
A: A regular N-gon is a polygon with N sides of equal length and N angles of equal measure.

Q2: Does this formula work for all regular polygons?
A: Yes, this formula works for all regular polygons with 3 or more sides.

Q3: What is the relationship between inradius and circumradius?
A: The inradius is always smaller than the circumradius (radius of the circumscribed circle) for any regular polygon.

Q4: How does the inradius change with increasing number of sides?
A: As the number of sides increases, the inradius approaches the circumradius, and for a circle (infinite sides), they become equal.

Q5: Can this calculator handle decimal values for number of sides?
A: No, the number of sides must be an integer value of 3 or greater.