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Perimeter Of Hendecagon Given Circumradius Formula:
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The formula calculates the perimeter of a hendecagon (11-sided polygon) when the circumradius (distance from center to vertex) is known. This geometric relationship uses trigonometric functions to determine the side length and total perimeter.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric properties of a regular hendecagon, where each side subtends an angle of \(2\pi/11\) at the center, and the side length can be expressed as \(2r_c\sin(\pi/11)\).
Details: Calculating the perimeter of geometric shapes is fundamental in various fields including architecture, engineering, and mathematics. For regular polygons like hendecagons, knowing the circumradius allows precise determination of the total boundary length.
Tips: Enter the circumradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding perimeter of the hendecagon.
Q1: What is a hendecagon?
A: A hendecagon is a polygon with eleven sides and eleven angles. When all sides and angles are equal, it's called a regular hendecagon.
Q2: How is the circumradius related to the side length?
A: In a regular hendecagon, the relationship between circumradius (r_c) and side length (s) is given by \( s = 2r_c\sin(\pi/11) \).
Q3: Can this formula be used for irregular hendecagons?
A: No, this formula applies only to regular hendecagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, construction planning, and geometric modeling where regular hendecagonal shapes are involved.
Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and trigonometric functions, providing highly accurate results when correct input values are provided.