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The Side of Decagon given Diagonal across Three Sides is a geometric calculation that determines the length of one side of a regular decagon when the diagonal spanning three sides is known. This formula is derived from the properties of regular polygons and their geometric relationships.
The calculator uses the formula:
Where:
Explanation: The formula utilizes the mathematical constant √5 and a specific denominator expression to calculate the side length from the given diagonal measurement.
Details: Calculating the side length of a decagon is essential in various geometric applications, architectural designs, and engineering projects where regular decagonal shapes are used. It helps in determining the precise dimensions and proportions of decagonal structures.
Tips: Enter the diagonal across three sides measurement in meters. The value must be positive and greater than zero. The calculator will compute the corresponding side length of the decagon.
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: Why is the formula structured this way?
A: The formula structure comes from geometric relationships and trigonometric properties specific to regular decagons, involving the golden ratio (φ) which is related to √5.
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 architecture (designing decagonal buildings), engineering (creating decagonal components), and various geometric design applications.
Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular decagons. The accuracy of the result depends on the precision of the input diagonal measurement.