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Perimeter Of Decagon Given Circumradius Formula:
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The Perimeter Of Decagon Given Circumradius formula calculates the total distance around a regular decagon when the circumradius (radius of the circumscribed circle) is known. This formula is derived from the geometric properties of regular polygons.
The calculator uses the Perimeter Of Decagon Given Circumradius formula:
Where:
Explanation: The formula relates the circumradius of a regular decagon to its perimeter through the mathematical constant φ (phi), where φ = (1 + √5)/2.
Details: Calculating the perimeter of a decagon is essential in various fields including architecture, engineering, and geometry. It helps in determining material requirements, boundary measurements, and structural design parameters for decagonal shapes.
Tips: Enter the circumradius value in meters. The value must be positive and greater than zero. The calculator will compute the perimeter based on the mathematical relationship between circumradius and perimeter in a regular decagon.
Q1: What is a regular decagon?
A: A regular decagon is a polygon with 10 equal sides and 10 equal angles. All vertices lie on a common circumscribed circle.
Q2: How is this formula derived?
A: The formula is derived from the relationship between the circumradius and side length of a regular decagon, using trigonometric functions and the golden ratio properties.
Q3: Can this calculator be used for irregular decagons?
A: No, this calculator is specifically designed for regular decagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, construction planning, manufacturing processes, and various engineering applications where decagonal shapes are involved.
Q5: How accurate is the calculation?
A: The calculation is mathematically precise for regular decagons. The accuracy depends on the precision of the input circumradius value.