1. What is Long Diagonal of Hexagon given Perimeter?

The Long Diagonal of a Hexagon is the length of the line joining any pair of opposite vertices. Given the perimeter, it can be calculated using a simple formula that relates the perimeter to the long diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d_{Long} \) — Long Diagonal of Hexagon (m)
• \( P \) — Perimeter of Hexagon (m)

Explanation: This formula derives from the fact that a regular hexagon can be divided into 6 equilateral triangles, and the long diagonal spans two of these triangles.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is important in geometry, architecture, and engineering for determining the maximum span across a hexagonal structure and for various design calculations.

4. Using the Calculator

Tips: Enter the perimeter of the hexagon in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for all hexagons?
A: This formula applies specifically to regular hexagons where all sides and angles are equal.

Q2: What is the relationship between side length and long diagonal?
A: For a regular hexagon, the long diagonal is exactly twice the side length (dLong = 2 × s).

Q3: How is the perimeter related to the side length?
A: For a regular hexagon, perimeter P = 6 × s, where s is the side length.

Q4: Can this calculator be used for irregular hexagons?
A: No, this calculator is designed specifically for regular hexagons. Irregular hexagons require more complex calculations.

Q5: What are some practical applications of this calculation?
A: This calculation is useful in construction, mechanical engineering, and design where hexagonal shapes are used, such as in bolts, nuts, and architectural elements.