1. What is Circumradius of Decagon?

The circumradius of a decagon is the radius of a circumcircle that touches all vertices of the decagon. It is an important geometric property that helps in understanding the spatial relationships and dimensions of regular decagons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( rc \) — Circumradius of Decagon (m)
• \( A \) — Area of Decagon (m²)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the circumradius based on the area of a regular decagon, incorporating the golden ratio (φ = (1+√5)/2) and geometric relationships specific to decagons.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing and analyzing decagonal structures, determining spatial requirements, and understanding the geometric properties of regular polygons.

4. Using the Calculator

Tips: Enter the area of the decagon in square meters. The value must be positive and greater than zero for accurate calculation.

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. All vertices lie on a common circumcircle.

Q2: How is the circumradius related to the side length?
A: For a regular decagon with side length s, the circumradius rc = s/2 × (1+√5) = s × φ, where φ is the golden ratio.

Q3: Can this calculator be used for irregular decagons?
A: No, this formula is specifically 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, engineering projects, and geometric analysis where decagonal shapes are involved.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular decagons, though real-world measurements may introduce some margin of error.