1. What is the Pentagon Side Formula?

The formula calculates the length of a side of a regular pentagon given its radius (distance from center to vertex). A regular pentagon has five equal sides and five equal angles.

2. How Does the Calculator Work?

The calculator uses the pentagon side formula:

Where:

• \( r \) — Radius of the pentagon (distance from center to vertex)
• \( \pi \) — Mathematical constant Pi (~3.14159)
• \( \sin \) — Trigonometric sine function

Explanation: The formula derives from dividing the pentagon into five isosceles triangles and using trigonometric relationships.

3. Importance of Pentagon Calculations

Details: Calculating pentagon side lengths is essential in geometry, architecture, and design where pentagonal shapes are used.

4. Using the Calculator

Tips: Enter the radius of the pentagon in any units. The result will be in the same units. Value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular pentagon?
A: A five-sided polygon with all sides equal and all angles equal (108° each).

Q2: What's the difference between radius and apothem?
A: Radius is center-to-vertex distance; apothem is center-to-side distance.

Q3: Can I calculate area with this?
A: No, this calculates side length. Area requires a different formula.

Q4: What if my pentagon isn't regular?
A: This formula only works for regular pentagons with equal sides and angles.

Q5: What's the exact value of sin(π/5)?
A: sin(π/5) = sin(36°) ≈ 0.5877852522924731.