1. What is Circumradius of Pentagon?

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of a regular 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 Circumradius of Pentagon formula:

Where:

• \( r_c \) — Circumradius of Pentagon (m)
• \( P \) — Perimeter of Pentagon (m)

Explanation: This formula calculates the circumradius based on the perimeter of a regular pentagon, using the mathematical relationship between the side length and the circumradius.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important 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 perimeter of the pentagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle?
A: A circumcircle is a circle that passes through all the vertices of a polygon. For a regular pentagon, the circumcircle touches all five vertices.

Q2: How is this formula derived?
A: The formula is derived from the relationship between the side length of a regular pentagon and its circumradius, combined with the perimeter formula P = 5 × side.

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 circumradius calculation?
A: Applications include architectural design, mechanical engineering, computer graphics, and any field requiring precise geometric calculations with pentagonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular pentagons, with accuracy limited only by the precision of the input values and computational rounding.