Edge Length of Hexagon given Inradius Calculator

Formula Used:

\[ Edge\ Length\ of\ Hexagon = \frac{2 \times Inradius\ of\ Hexagon}{\sqrt{3}} \] \[ l_e = \frac{2 \times r_i}{\sqrt{3}} \]

Edge Length of Hexagon:

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1. What is the Edge Length of Hexagon given Inradius?

The edge length of a regular hexagon can be calculated from its inradius using the mathematical relationship between these two geometric properties. The inradius is the radius of the circle inscribed within the hexagon that touches all six sides.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Edge\ Length\ of\ Hexagon = \frac{2 \times Inradius\ of\ Hexagon}{\sqrt{3}} \]

Where:

\( Inradius\ of\ Hexagon \) — The radius of the inscribed circle (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the geometric properties of a regular hexagon, where the relationship between the edge length and inradius is fixed and can be expressed using basic trigonometric principles.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from the inradius is important in various geometric and engineering applications, particularly in designing hexagonal structures, tiling patterns, and understanding the spatial properties of regular hexagons.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the 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: What is the inradius of a hexagon?
A: The inradius is the radius of the largest circle that can fit inside the hexagon, touching all six sides.

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 engineering design, architecture, material science, and any field dealing with hexagonal patterns or structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexagons, as it's derived from geometric principles.