1. What is a Regular Hexagon?

A regular hexagon is a six-sided polygon where all sides are equal in length and all internal angles are equal to 120 degrees. It's a highly symmetrical shape found in nature (honeycombs) and human designs.

2. How Does the Calculator Work?

The calculator uses the hexagon area formula:

Where:

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

Explanation: The formula calculates the area of a regular hexagon by dividing it into 6 equilateral triangles and summing their areas.

3. Properties of Regular Hexagons

Details: Regular hexagons have several interesting properties: all internal angles measure 120°, they can tile a plane without gaps, and they have the highest area-to-perimeter ratio of any regular polygon.

4. Using the Calculator

Tips: Enter the side length of the hexagon in any consistent unit of measurement. The result will be in square units of that same measurement.

5. Frequently Asked Questions (FAQ)

Q1: What is the internal angle of a regular hexagon?
A: Each internal angle of a regular hexagon measures exactly 120 degrees.

Q2: How do you calculate the perimeter of a hexagon?
A: The perimeter of a regular hexagon is simply 6 times the side length (P = 6s).

Q3: Can this calculator be used for irregular hexagons?
A: No, this calculator is specifically for regular hexagons where all sides and angles are equal.

Q4: What is the apothem of a regular hexagon?
A: The apothem (distance from center to midpoint of a side) is equal to \( \frac{\sqrt{3}}{2} s \), or approximately 0.866 times the side length.

Q5: How is the area formula derived?
A: The formula comes from dividing the hexagon into 6 equilateral triangles, each with area \( \frac{\sqrt{3}}{4} s^2 \), then multiplying by 6 and simplifying.