1. What is a Regular Polygon?

A regular polygon is a geometric shape with all sides and all angles equal. Examples include equilateral triangles, squares, regular pentagons, etc. The area can be calculated when you know the number of sides and the length of one side.

2. How Does the Calculator Work?

The calculator uses the regular polygon area formula:

Where:

• \( A \) — Area of the polygon
• \( n \) — Number of sides (must be ≥3)
• \( s \) — Length of one side
• \( \pi \) — Pi constant (~3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the area by dividing the polygon into n congruent isosceles triangles and summing their areas.

3. Importance of Regular Polygons

Details: Regular polygons are fundamental shapes in geometry, architecture, and design. Understanding their properties is essential in many fields including engineering, computer graphics, and crystallography.

4. Using the Calculator

Tips: Enter the number of sides (must be 3 or greater) and the side length (must be positive). The calculator will compute the area of the regular polygon.

5. Frequently Asked Questions (FAQ)

Q1: What's the minimum number of sides?
A: A polygon must have at least 3 sides (triangle). The calculator requires n ≥ 3.

Q2: What units does the calculator use?
A: The area will be in whatever squared units your side length was in (e.g., cm² if side was in cm).

Q3: How accurate is the calculation?
A: The calculator provides results rounded to 4 decimal places using precise trigonometric functions.

Q4: Can I calculate properties other than area?
A: This calculator focuses on area, but other properties like apothem and perimeter can be derived from these inputs.

Q5: What about very large numbers of sides?
A: As n approaches infinity, the shape approaches a circle. The calculator works for any integer n ≥ 3.