1. What is the Inradius of Hexagon?

The Inradius of Hexagon is the radius of the incircle of a regular hexagon, which is the largest circle that can fit inside the hexagon and touch all six sides. For a regular hexagon, the inradius is directly proportional to the edge length.

2. How Does the Calculator Work?

The calculator uses the Inradius of Hexagon formula:

Where:

• \( r_i \) — Inradius of Hexagon (m)
• \( l_e \) — Edge Length of Hexagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula shows that the inradius of a regular hexagon is equal to the edge length multiplied by the constant factor √3/2.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry, engineering, and design applications where hexagonal shapes are used. It helps determine the maximum size of circular components that can fit inside a hexagonal structure.

4. Using the Calculator

Tips: Enter the edge length of the hexagon in meters. The value must be positive and valid. The calculator will compute the inradius based on the mathematical relationship between edge length and inradius in a regular hexagon.

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 inradius related to the circumradius?
A: In a regular hexagon, the inradius (r) and circumradius (R) are related by the formula: R = 2r/√3, or equivalently, r = R√3/2.

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

Q4: What are some practical applications of this calculation?
A: This calculation is useful in mechanical engineering (bolt heads, nuts), architecture (hexagonal tiles), and materials science (honeycomb structures).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular hexagons. The accuracy in practical applications depends on the precision of the edge length measurement.