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The formula calculates the perimeter of a hendecagon (11-sided polygon) when the inradius (radius of the inscribed circle) is known. This geometric relationship helps in determining the total boundary length of a regular hendecagon.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric properties of a regular hendecagon, where the tangent function relates the inradius to the side length through the central angle.
Details: Calculating the perimeter of geometric shapes is fundamental in various fields including architecture, engineering, and mathematics. For regular polygons like hendecagons, knowing the perimeter helps in material estimation, construction planning, and spatial analysis.
Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding perimeter of the regular hendecagon.
Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. When all sides and angles are equal, it's called a regular hendecagon.
Q2: What is the inradius of a polygon?
A: The inradius is the radius of the largest circle that fits inside the polygon, tangent to all its sides.
Q3: Why is the tangent function used in this formula?
A: The tangent function relates the inradius to the side length through the central angle (π/11 radians) of the regular hendecagon.
Q4: Can this formula be used for irregular hendecagons?
A: No, this formula applies only to regular hendecagons where all sides and angles are equal.
Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, manufacturing of polygonal components, and mathematical research involving regular polygons.