1. What is Apothem of a Hexagon?

The apothem of a regular hexagon is the distance from the center to the midpoint of any side. It is perpendicular to that side and represents the radius of the inscribed circle.

2. How Does the Calculator Work?

The calculator uses the apothem formula for regular hexagon:

Where:

• \( a \) — Apothem length
• \( s \) — Side length of the hexagon
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the equilateral triangles that form a regular hexagon when divided from the center to vertices.

3. Importance of Apothem Calculation

Details: The apothem is crucial for calculating the area of regular polygons (Area = ½ × Perimeter × Apothem) and has applications in engineering, architecture, and geometry problems.

4. Using the Calculator

Tips: Enter the side length of the regular hexagon. The value must be positive and greater than zero. The calculator will compute the apothem using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hexagon?
A: A regular hexagon is a six-sided polygon where all sides are equal in length and all interior angles are equal (120 degrees each).

Q2: How is apothem different from radius?
A: The radius is the distance from center to vertex, while apothem is the distance from center to the midpoint of a side. For a hexagon, radius equals side length.

Q3: Can this formula be used for irregular hexagons?
A: No, this formula only applies to regular hexagons where all sides and angles are equal.

Q4: What are practical applications of apothem?
A: Used in construction (hexagonal tiles, nuts), engineering (honeycomb structures), and geometry calculations for area and perimeter.

Q5: How does apothem relate to area calculation?
A: Area of regular polygon = ½ × Perimeter × Apothem. For hexagon: Area = (3√3/2) × s² = 3 × s × a.