1. What is the Apothem Calculator?

The Apothem Calculator determines the apothem length of a regular polygon using the side length and number of sides. The apothem is the distance from the center to the midpoint of any side of a regular polygon.

2. How Does the Calculator Work?

The calculator uses the apothem formula:

Where:

• \( a \) — Apothem length
• \( s \) — Side length of the polygon
• \( n \) — Number of sides

Explanation: The formula calculates the apothem by dividing the side length by twice the tangent of the central angle (180/n degrees).

3. Importance of Apothem Calculation

Details: The apothem is crucial for calculating the area of regular polygons (Area = ½ × Perimeter × Apothem) and is used in various geometric and architectural applications.

4. Using the Calculator

Tips: Enter the side length and number of sides (must be at least 3). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular polygon?
A: A regular polygon has all sides equal and all angles equal, such as equilateral triangles, squares, pentagons, etc.

Q2: Can this calculator be used for irregular polygons?
A: No, this calculator only works for regular polygons where all sides and angles are equal.

Q3: What units should I use?
A: Use any consistent unit of measurement (cm, inches, meters, etc.) for both input and output values.

Q4: Why does the number of sides need to be at least 3?
A: A polygon must have at least 3 sides to form a closed shape.

Q5: How is apothem related to the circumradius?
A: In a regular polygon, the apothem equals the circumradius multiplied by the cosine of 180/n degrees.