1. What is the Side of Hexadecagon given Inradius Formula?

The formula calculates the side length of a regular hexadecagon (16-sided polygon) when the inradius (radius of the inscribed circle) is known. This geometric relationship is important in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side of Hexadecagon (m)
• \( r_i \) — Inradius of Hexadecagon (m)

Explanation: The formula derives from the geometric properties of a regular hexadecagon and its relationship with the inscribed circle.

3. Importance of Hexadecagon Side Calculation

Details: Calculating the side length from the inradius is crucial in geometric design, architectural planning, and various engineering applications where regular polygonal shapes are used.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hexadecagon?
A: A regular hexadecagon is a 16-sided polygon where all sides are equal in length and all angles are equal.

Q2: What is the relationship between inradius and side length?
A: The inradius is the radius of the circle that fits perfectly inside the hexadecagon, touching all sides at their midpoints.

Q3: Can this formula be used for irregular hexadecagons?
A: No, this formula applies only to regular hexadecagons where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric pattern creation.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hexadecagons, though real-world measurements may have practical limitations.