1. What is the Circumradius of Pentagon?

The circumradius of a pentagon is the radius of the circumscribed circle that passes through all five vertices of the pentagon. It represents the distance from the center of the pentagon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( rc \) — Circumradius of Pentagon (m)
• \( A \) — Area of Pentagon (m²)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives the circumradius from the area of a regular pentagon using mathematical relationships between the pentagon's geometric properties.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing pentagonal structures, determining spatial relationships, and solving geometric problems involving regular pentagons.

4. Using the Calculator

Tips: Enter the area of the pentagon 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 pentagon?
A: A regular pentagon is a five-sided polygon where all sides are equal in length and all interior angles are equal (108 degrees each).

Q2: How is the circumradius related to the side length?
A: For a regular pentagon with side length s, the circumradius can also be calculated as \( rc = \frac{s}{10} \times \sqrt{50 + 10\sqrt{5}} \).

Q3: Can this calculator be used for irregular pentagons?
A: No, this calculator is specifically designed for regular pentagons where all sides and angles are equal.

Q4: What are practical applications of pentagon circumradius?
A: Applications include architectural design (pentagonal buildings), mechanical engineering (pentagonal components), and mathematical modeling.

Q5: How accurate is the calculation?
A: The calculation provides high mathematical accuracy, with results rounded to 12 decimal places for precision.