1. What is the Perimeter of Pentagon given Circumradius Formula?

The formula calculates the perimeter of a regular pentagon when the circumradius (radius of the circumscribed circle) is known. It provides an accurate measurement of the total distance around the pentagon's edges.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula derives from the geometric properties of a regular pentagon and its relationship with the circumscribed circle.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a pentagon is essential in various geometric applications, architectural design, and engineering projects involving pentagonal shapes.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumradius in a pentagon?
A: The circumradius is the radius of a circle that passes through all the vertices of the pentagon.

Q2: Does this formula work for irregular pentagons?
A: No, this formula is specifically for regular pentagons where all sides and angles are equal.

Q3: What are typical circumradius values for pentagons?
A: Circumradius values depend on the size of the pentagon. For a regular pentagon with side length s, the circumradius is s/√(5-2√5).

Q4: Can I use this calculator for pentagons with different units?
A: The calculator uses meters as the default unit, but you can use any consistent unit as long as you maintain the same unit for both input and output.

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