Inradius of Hexadecagon Formula:
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The inradius of a hexadecagon (16-sided polygon) is the radius of the circle that fits perfectly inside the hexadecagon, touching all its sides. It represents the distance from the center of the hexadecagon to any of its sides.
The calculator uses the formula:
Where:
Explanation: This formula calculates the exact inradius of a regular hexadecagon based on its side length, incorporating the mathematical relationships between the polygon's geometry and its inscribed circle.
Details: Calculating the inradius is important in geometry and various practical applications such as architecture, engineering design, and manufacturing where precise measurements of regular polygons are required.
Tips: Enter the side length of the hexadecagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding inradius.
Q1: What is a regular hexadecagon?
A: A regular hexadecagon is a 16-sided polygon where all sides are equal in length and all interior angles are equal (157.5 degrees each).
Q2: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching the sides), while the circumradius is the radius of the circumscribed circle (passing through the vertices).
Q3: Can this formula be used for irregular hexadecagons?
A: No, this formula is specifically for regular hexadecagons where all sides and angles are equal. Irregular hexadecagons require different calculation methods.
Q4: What are practical applications of hexadecagons?
A: Hexadecagons are used in various fields including architecture (building designs), engineering (mechanical parts), and design (decorative patterns).
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexadecagons, with accuracy limited only by the precision of the input value and computational floating-point arithmetic.