1. What is the Inradius of a Decagon?

The inradius of a decagon is the radius of the incircle (the circle that fits perfectly inside the decagon and touches all its sides). It is the perpendicular distance from the center to any side of the decagon.

2. How Does the Calculator Work?

The calculator uses the Inradius of Decagon formula:

Where:

• \( r_i \) — Inradius of Decagon
• \( S \) — Side length of the Decagon
• \( \sqrt{} \) — Square root function

Explanation: The formula calculates the inradius based on the side length of a regular decagon, incorporating the mathematical constant relationships specific to a 10-sided polygon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the incircle, which is useful in various applications including construction, design, and mathematical analysis of regular decagons.

4. Using the Calculator

Tips: Enter the side length of the decagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a decagon?
A: A decagon is a polygon with ten sides and ten angles. A regular decagon has all sides equal and all angles equal.

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

Q3: Can this calculator be used for irregular decagons?
A: No, this formula is specifically for regular decagons where all sides and angles are equal.

Q4: What are practical applications of inradius calculation?
A: Inradius calculations are used in architecture, engineering design, and various geometric constructions involving regular polygons.

Q5: How accurate is the calculated result?
A: The result is mathematically precise for the given input, with rounding to 6 decimal places for clarity.