1. What is a Decagon?

A decagon is a ten-sided polygon with ten angles. In a regular decagon, all sides are equal in length and all angles are equal in measure (144° each).

2. How Does the Calculator Work?

The calculator uses the decagon side length formula:

Where:

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

Explanation: The formula calculates the length of each side of a regular decagon based on its circumradius.

3. Importance of Decagon Calculations

Details: Calculating decagon dimensions is important in geometry, architecture, and design where ten-sided symmetrical shapes are needed.

4. Using the Calculator

Tips: Enter the radius (distance from center to any vertex) in length units. The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radius and apothem?
A: Radius is center-to-vertex distance, while apothem is center-to-midpoint distance of a side.

Q2: How do I calculate decagon area?
A: Area = (5/2) × side² × cot(π/10) or 2.5 × side × apothem.

Q3: What's the interior angle of a regular decagon?
A: Each interior angle is 144° (calculated by (n-2)×180°/n where n=10).

Q4: Can this calculator work for irregular decagons?
A: No, this calculator only works for regular (equilateral and equiangular) decagons.

Q5: What's the exact value of sin(π/10)?
A: sin(π/10) = (√5 - 1)/4 ≈ 0.309016994.