1. What is 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)
• \( d_{Short} \) — Short Diagonal of Hexagon (m)

Explanation: The inradius of a regular hexagon can be directly calculated from the short diagonal by dividing it by 2.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various practical applications such as construction, design, and engineering where hexagonal shapes are used. It helps in determining the size of the largest circle that can fit inside the hexagon.

4. Using the Calculator

Tips: Enter the Short Diagonal of 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 short diagonal related to the side length?
A: In a regular hexagon, the short diagonal is equal to \( \sqrt{3} \) times the side length.

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

Q4: What are some practical applications of hexagons?
A: Hexagons are used in various fields including engineering, architecture, nature (honeycombs), and design due to their efficient space-filling properties.

Q5: How does the inradius relate to the circumradius?
A: In a regular hexagon, the inradius is \( \frac{\sqrt{3}}{2} \) times the side length, while the circumradius equals the side length.