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Long Diagonal of Hexagon Formula:
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The Long Diagonal of a Hexagon is the length of the line joining any pair of opposite vertices of the Hexagon. In a regular hexagon, all long diagonals are equal in length and pass through the center of the hexagon.
The calculator uses the Long Diagonal of Hexagon formula:
Where:
Explanation: The long diagonal of a regular hexagon is exactly twice the length of its edge. This relationship holds true for all regular hexagons regardless of size.
Details: Calculating the long diagonal is essential in various geometric applications, architectural designs, engineering projects, and mathematical problems involving hexagonal shapes. It helps in determining the overall dimensions and spatial requirements of hexagonal structures.
Tips: Enter the edge length of the hexagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding long diagonal length.
Q1: Is this formula applicable to all hexagons?
A: This formula specifically applies to regular hexagons where all sides and angles are equal. For irregular hexagons, the long diagonal lengths may vary.
Q2: What is the relationship between long diagonal and short diagonal?
A: In a regular hexagon, the long diagonal is exactly twice the edge length, while the short diagonal is \( \sqrt{3} \) times the edge length.
Q3: Can this calculator be used for hexagonal prisms?
A: This calculator computes the 2D long diagonal of a regular hexagon. For 3D hexagonal prisms, additional calculations would be needed for spatial diagonals.
Q4: What are common applications of hexagonal geometry?
A: Hexagonal patterns are widely used in engineering, architecture, materials science (honeycomb structures), and graphic design due to their efficient packing properties.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexagons. The accuracy depends on the precision of the input edge length measurement.