1. What is the Decagon Side Length Formula?

The decagon side length formula calculates the length of each side of a regular decagon (10-sided polygon) given its radius (distance from center to vertex).

2. How Does the Calculator Work?

The calculator uses the decagon side length formula:

Where:

• \( s \) — Side length of the decagon
• \( r \) — Radius of the decagon (distance from center to vertex)
• \( \pi \) — Mathematical constant Pi (~3.14159)

Explanation: The formula derives from dividing the decagon into 10 isosceles triangles and using trigonometric relationships.

3. Importance of Decagon Side Calculation

Details: Calculating side length is essential in geometry, architecture, and design when working with decagonal shapes. It helps in construction and material estimation.

4. Using the Calculator

Tips: Enter the radius of the decagon in any length units. The result will be in the same units. The radius must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a 10-sided polygon with all sides equal and all angles equal (144° each).

Q2: What's the difference between radius and apothem?
A: Radius is center-to-vertex distance, while apothem is center-to-side distance. They're related but different measurements.

Q3: Can I calculate the radius if I know the side length?
A: Yes, you can rearrange the formula: \( r = \frac{s}{2 \times \sin(\pi/10)} \).

Q4: What is the exact value of sin(π/10)?
A: \( \sin(\pi/10) = \frac{\sqrt{5} - 1}{4} \approx 0.309016994 \).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular decagon. Real-world accuracy depends on measurement precision.