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The formula calculates the side length of a regular dodecagon (12-sided polygon) when given the length of the diagonal that spans across two sides. This relationship is derived from the geometric properties of regular polygons.
The calculator uses the formula:
Where:
Explanation: The formula uses the mathematical constants √2 and √6 to establish the precise relationship between the side length and the diagonal measurement in a regular dodecagon.
Details: Calculating the side length of a dodecagon is essential in geometry, architecture, and engineering applications where regular dodecagonal shapes are used. It helps in determining material requirements, structural properties, and spatial planning.
Tips: Enter the diagonal measurement across two sides in meters. The value must be positive and greater than zero. The calculator will compute the corresponding side length of the regular dodecagon.
Q1: What is a regular dodecagon?
A: A regular dodecagon is a 12-sided polygon where all sides are equal in length and all interior angles are equal (150 degrees each).
Q2: How accurate is this calculation?
A: The calculation is mathematically precise for perfect regular dodecagons, using exact mathematical constants and relationships.
Q3: Can this formula be used for irregular dodecagons?
A: No, this formula specifically applies to regular dodecagons where all sides and angles are equal.
Q4: What are practical applications of dodecagon calculations?
A: Dodecagons are used in architecture (building designs), engineering (structural components), and various decorative patterns and designs.
Q5: How does the diagonal relate to the side length?
A: In a regular dodecagon, the diagonal spanning two sides maintains a constant mathematical relationship with the side length, expressed through the formula using √2 and √6.