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Perimeter of Decagon Formula:
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The formula calculates the perimeter of a regular decagon when given the diagonal length across five sides. A decagon is a ten-sided polygon, and this specific formula relates the perimeter to the diagonal measurement.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric properties of regular decagons and the golden ratio relationship between side lengths and diagonals.
Details: Calculating the perimeter of geometric shapes is fundamental in various fields including architecture, engineering, and mathematics. For decagons, perimeter calculations help in material estimation, structural design, and spatial planning.
Tips: Enter the diagonal measurement across five sides in meters. The value must be positive and greater than zero. The calculator will compute the perimeter using the mathematical relationship.
Q1: What is a regular decagon?
A: A regular decagon is a ten-sided polygon where all sides are equal in length and all interior angles are equal (144 degrees each).
Q2: How is the diagonal across five sides defined?
A: The diagonal across five sides connects two non-adjacent vertices with five sides between them, representing the longest diagonal in a regular decagon.
Q3: Can this formula be used for irregular decagons?
A: No, this formula applies only to regular decagons where all sides and angles are equal. Irregular decagons require different calculation methods.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, manufacturing of decagonal objects, mathematical modeling, and geometric problem solving.
Q5: How accurate is the calculation?
A: The calculation is mathematically exact for regular decagons. The accuracy depends on the precision of the input diagonal measurement.