1. What is the Inradius of Hexagon?

The Inradius of a Hexagon is the radius of the incircle of the Hexagon or the circle that is contained by the Hexagon with all edges touching the circle. It represents the distance from the center of the hexagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Hexagon (m)
• \( A_{\text{Equilateral Triangle}} \) — Area of Equilateral Triangle of Hexagon (m²)

Explanation: This formula calculates the inradius of a regular hexagon based on the area of one of its equilateral triangles, utilizing the mathematical relationship between triangle area and hexagon geometry.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and engineering applications where the relationship between a hexagon's area and its inscribed circle is needed for design and analysis purposes.

4. Using the Calculator

Tips: Enter the area of the equilateral triangle in square meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hexagon?
A: A regular hexagon is a six-sided polygon where all sides are equal in length and all interior angles are equal to 120 degrees.

Q2: How is the inradius related to the side length?
A: For a regular hexagon with side length s, the inradius is \( \frac{s\sqrt{3}}{2} \).

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

Q4: What are practical applications of hexagon inradius calculations?
A: Hexagon geometry is used in various fields including engineering design, architecture, material science, and honeycomb structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hexagons, with accuracy depending on the precision of the input values.