1. What is Circumradius of Hexagon?

The circumradius of a hexagon is the radius of the circumscribed circle that passes through all the vertices of the hexagon. It represents the distance from the center of the hexagon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of the hexagon
• \( A \) — Area of the hexagon
• \( \sqrt{} \) — Square root function

Explanation: This formula derives from the relationship between the area of a regular hexagon and its circumradius, using mathematical constants and geometric properties.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, engineering, and design applications where hexagons are used. It helps determine the size and proportions of hexagonal structures and patterns.

4. Using the Calculator

Tips: Enter the area of the hexagon in square meters. The value must be positive and greater than zero for accurate calculation.

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 circumradius different from inradius?
A: Circumradius is the radius of the circumscribed circle passing through vertices, while inradius is the radius of the inscribed circle tangent to the sides.

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

Q4: What are practical applications of hexagon circumradius?
A: Used in engineering design, architecture, honeycomb structures, bolt patterns, and various geometric constructions.

Q5: How does area relate to circumradius in a hexagon?
A: The area of a regular hexagon is directly proportional to the square of its circumradius, following a specific mathematical relationship.