1. What is the Side of Decagon given Circumradius Formula?

The formula calculates the side length of a regular decagon when its circumradius is known. A regular decagon is a ten-sided polygon with all sides and angles equal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side of Decagon (m)
• \( r_c \) — Circumradius of Decagon (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives from the geometric properties of a regular decagon and its relationship with the golden ratio.

3. Importance of Side Calculation

Details: Calculating the side length of a decagon is essential in geometry, architecture, and design applications where regular decagonal shapes are used.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a polygon with ten equal sides and ten equal angles.

Q2: What is circumradius?
A: Circumradius is the radius of a circle that passes through all vertices of a polygon.

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.

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

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular decagons and provides precise results when correct values are input.