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The formula calculates the side length of a regular dodecagon (12-sided polygon) when the inradius (radius of the inscribed circle) is known. It provides a precise geometric relationship between these two properties 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 side length and the radius of its inscribed circle.
Details: Calculating the side length from the inradius is crucial in geometric design, architecture, and engineering applications involving dodecagonal shapes. It helps in determining the precise dimensions of dodecagonal structures and components.
Tips: Enter the inradius value 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 accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular dodecagon, using the precise geometric relationship between side length and inradius.
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 this calculation?
A: This calculation is useful in architectural design, mechanical engineering, and any field requiring precise geometric measurements of dodecagonal shapes.
Q5: How does the inradius relate to other dodecagon properties?
A: The inradius is directly related to the side length, circumradius, and area of a regular dodecagon through specific geometric formulas.