Inradius of Hexagon given Width Calculator

Inradius of Hexagon Formula:

\[ r_i = \frac{\sqrt{3} \times w}{4} \]

Inradius of Hexagon:

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1. What is the Inradius of Hexagon?

The inradius of a hexagon is the radius of the largest circle that can be inscribed within the hexagon, touching all six sides. 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 inradius formula:

\[ r_i = \frac{\sqrt{3} \times w}{4} \]

Where:

\( r_i \) — Inradius of the hexagon
\( w \) — Width of the hexagon (distance between opposite vertices)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the geometric properties of a regular hexagon, where the width represents the distance between two opposite vertices.

3. Importance of Inradius Calculation

Details: Calculating the inradius is essential in various geometric applications, including determining the size of inscribed circles, optimizing material usage in hexagonal designs, and solving problems in engineering and architecture involving hexagonal structures.

4. Using the Calculator

Tips: Enter the width of the hexagon in meters. The width must be a positive value greater than zero. The calculator will compute the corresponding inradius.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between width and inradius?
A: The inradius is directly proportional to the width of the hexagon, with a constant factor of √3/4.

Q2: Can this formula be used for irregular hexagons?
A: No, this formula applies only to regular hexagons where all sides and angles are equal.

Q3: How is width different from side length?
A: Width is the distance between two opposite vertices, while side length is the length of one edge of the hexagon.

Q4: What are practical applications of this calculation?
A: Used in engineering for bolt head designs, in architecture for hexagonal tiles and structures, and in mathematics for geometric problem solving.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexagons, with accuracy limited only by the precision of the input values and computational rounding.