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The formula calculates the perimeter of a regular nonagon (9-sided polygon) when the circumradius (distance from center to vertex) is known. This geometric relationship helps in determining the total boundary length of a nonagon.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric properties of a regular nonagon, where each side can be expressed in terms of the circumradius and the central angle (40° or π/9 radians).
Details: Calculating the perimeter of geometric shapes is fundamental in various fields including architecture, engineering, and mathematics. For regular polygons like nonagons, 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 perimeter using the trigonometric relationship.
Q1: What is a regular nonagon?
A: A regular nonagon is a nine-sided polygon where all sides are equal in length and all interior angles are equal (140° each).
Q2: How is the circumradius related to the side length?
A: In a regular nonagon, the circumradius \( r_c \) relates to the side length \( s \) through the formula: \( s = 2 \times r_c \times \sin(\pi/9) \).
Q3: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, manufacturing of polygonal components, and geometric pattern creation.
Q5: How accurate is the trigonometric calculation?
A: The calculation is mathematically exact for ideal regular nonagons. Real-world measurements may introduce practical limitations.