1. What is the Area of Pentagon Formula?

The formula calculates the area of a regular pentagon using its circumradius. A regular pentagon is a five-sided polygon with all sides and angles equal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of the pentagon
• \( r_c \) — Circumradius of the pentagon
• \( \sqrt{} \) — Square root function

Explanation: This formula derives from the geometric properties of a regular pentagon and uses the circumradius to calculate the area directly.

3. Importance of Pentagon Area Calculation

Details: Calculating the area of a pentagon is important in geometry, architecture, and various engineering applications where pentagonal 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 circumradius?
A: The circumradius is the radius of a circle that passes through all the vertices of a polygon.

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

Q3: What are the units of measurement?
A: The circumradius should be entered in meters, and the area result will be in square meters.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for regular pentagons, though practical measurements may introduce some error.

Q5: Can I use this for other polygons?
A: No, this specific formula is designed only for regular pentagons. Other polygons have different area formulas.