1. What is the Inradius of Hexagon?

The Inradius of Hexagon is the radius of 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)
• \( d_{Long} \) — Long Diagonal of Hexagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula calculates the inradius of a regular hexagon based on its long diagonal, which connects opposite vertices through the center.

3. Importance of Inradius Calculation

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

4. Using the Calculator

Tips: Enter the long diagonal of the hexagon in meters. The value must be positive and greater than zero.

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 (120 degrees each).

Q2: How is the long diagonal related to the side length?
A: In a regular hexagon, the long diagonal is exactly twice the side length (dLong = 2 × side).

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

Q4: What are practical applications of hexagon geometry?
A: Hexagons are used in various fields including engineering (bolts, nuts), architecture (tiling patterns), and nature (honeycomb structures).

Q5: How does the inradius relate to the circumradius?
A: In a regular hexagon, the inradius (r) and circumradius (R) are related by the formula r = R × cos(30°) = R × √3/2.