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The short diagonal of a hexagon is the line segment connecting two non-adjacent vertices that have one vertex between them. In a regular hexagon, all short diagonals have equal length and are shorter than the long diagonals.
The calculator uses the formula:
Where:
Explanation: This formula derives from the relationship between the side length and diagonal length in a regular hexagon, where the perimeter is 6 times the side length.
Details: Calculating the short diagonal is important in geometry, engineering, and design applications involving hexagonal structures. It helps determine internal distances and spatial relationships within hexagonal patterns.
Tips: Enter the perimeter of the hexagon in meters. The value must be positive and greater than zero. The calculator will compute the short diagonal length.
Q1: Does this formula work for irregular hexagons?
A: No, this formula applies only to regular hexagons where all sides and angles are equal.
Q2: How is this formula derived?
A: The formula comes from the relationship between side length (s = P/6) and short diagonal length (s√3) in a regular hexagon.
Q3: What's the difference between short and long diagonals?
A: In a regular hexagon, short diagonals connect vertices with one vertex between them, while long diagonals connect opposite vertices and are twice the length of the side.
Q4: Can I use this for hexagonal prisms?
A: This calculates the 2D diagonal within the hexagonal face. For 3D diagonals in a prism, additional calculations involving height are needed.
Q5: What are practical applications of this calculation?
A: Used in engineering for bolt patterns, architectural design, honeycomb structures, and any application involving regular hexagonal geometry.