1. What is the Short Diagonal of Hexagon?

The short diagonal of a regular hexagon is the line segment connecting two non-adjacent vertices that have one vertex between them. In a regular hexagon, all short diagonals are equal in length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• \( \text{Width} \) — The horizontal distance between the leftmost and rightmost vertices of the hexagon

Explanation: This formula derives from the geometric properties of a regular hexagon, where the width equals twice the side length, and the short diagonal relates to the side length through trigonometric relationships.

3. Importance of Short Diagonal Calculation

Details: Calculating the short diagonal is essential in various geometric applications, architectural designs, engineering projects, and pattern-making where hexagonal shapes are used.

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 short diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between side length and width?
A: In a regular hexagon, the width equals twice the side length (Width = 2 × Side Length).

Q2: How does the short diagonal relate to the side length?
A: The short diagonal equals \( \sqrt{3} \) times the side length of the hexagon.

Q3: What is the difference between short and long diagonals?
A: The short diagonal connects vertices with one vertex between them, while the long diagonal connects opposite vertices (diameter).

Q4: Can this formula be used for irregular hexagons?
A: No, this formula applies only to regular hexagons where all sides and angles are equal.

Q5: What are practical applications of this calculation?
A: This calculation is used in engineering, architecture, game design, and any field working with hexagonal patterns or structures.