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The formula calculates the side length of a regular dodecagon (12-sided polygon) when its circumradius is known. It provides a precise mathematical relationship between the circumradius and side length of a regular dodecagon.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric properties of a regular dodecagon, specifically the relationship between its circumradius and side length through trigonometric functions.
Details: Accurate side length calculation is crucial for geometric construction, architectural design, and engineering applications involving dodecagonal shapes. It helps in determining perimeter, area, and other geometric properties.
Tips: Enter the circumradius in meters. The value must be positive and valid. 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 is the circumradius related to the side length?
A: The circumradius is the distance from the center to any vertex of the dodecagon, while the side length is the distance between two adjacent vertices.
Q3: Can this formula be used for irregular dodecagons?
A: No, this formula applies only to regular dodecagons where all sides and angles are equal.
Q4: What are practical applications of dodecagon calculations?
A: Dodecagons are used in architecture, coin design, clock faces, and various decorative patterns where symmetry is important.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal regular dodecagons, though practical measurements may have slight variations.