1. What is the Width of Hexagon given Inradius Formula?

The formula calculates the width of a regular hexagon when its inradius (the radius of the inscribed circle) is known. It provides a mathematical relationship between these two geometric properties of a hexagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( w \) — Width of Hexagon (m)
• \( r_i \) — Inradius of Hexagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula derives from the geometric properties of a regular hexagon, where the width is directly proportional to the inradius with a constant factor of \( \frac{4}{\sqrt{3}} \).

3. Importance of Hexagon Width Calculation

Details: Calculating the width of a hexagon from its inradius is crucial in various engineering, architectural, and design applications where hexagonal shapes are used, such as in bolt heads, nuts, and structural components.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding width of the 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 internal angles are 120 degrees.

Q2: What is the relationship between inradius and side length?
A: For a regular hexagon, the inradius \( r_i = \frac{\sqrt{3}}{2} \times \) 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 practical applications of this calculation?
A: This calculation is useful in mechanical engineering for designing hexagonal fasteners, in architecture for hexagonal tile patterns, and in various manufacturing processes.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular hexagons and provides precise results when accurate input values are provided.