1. What is the Polygon Side Length Formula?

The polygon side length formula calculates the length of each side of a regular polygon given its radius and number of sides. It's based on trigonometric relationships in regular polygons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( s \) — Side length (same units as radius)
• \( r \) — Circumradius (distance from center to vertex)
• \( n \) — Number of sides (integer ≥ 3)

Explanation: The formula divides the polygon into n isosceles triangles and uses trigonometry to calculate the base (side length) of each triangle.

3. Importance of Side Length Calculation

Details: Calculating side lengths is essential in geometry, architecture, and engineering for designing and constructing regular polygonal shapes.

4. Using the Calculator

Tips: Enter the radius in any length units (must be > 0) and number of sides (integer ≥ 3). The result will be in the same units as the radius.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for both apothem and circumradius?
A: This formula uses circumradius (vertex radius). For apothem (side radius), use a different formula.

Q2: What's the minimum number of sides?
A: The formula works for any regular polygon with 3 or more sides (triangle and above).

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular polygons.

Q4: Can I use this for star polygons?
A: No, this only works for simple regular polygons where sides don't intersect.

Q5: What units should I use?
A: Any consistent length units can be used (mm, cm, inches, etc.), just be consistent.