1. What is the Area of Hexagon given Circumradius?

The Area of Hexagon given Circumradius is the total quantity of plane enclosed by the boundary lines of a regular hexagon when the circumradius (radius of the circumscribed circle) is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of Hexagon (m²)
• \( r_c \) — Circumradius of Hexagon (m)

Explanation: This formula calculates the area of a regular hexagon by relating it to the circumradius, which is the distance from the center to any vertex.

3. Importance of Area Calculation

Details: Calculating the area of a hexagon is important in various fields including geometry, architecture, engineering, and material science where hexagonal patterns and structures are commonly used.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and valid.

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 to 120 degrees.

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle that passes through all vertices of the hexagon, while inradius is the radius of the circle inscribed within the hexagon.

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

Q4: What are practical applications of hexagonal area calculation?
A: Hexagonal area calculations are used in honeycomb structures, floor tiling, bolt head designs, and various engineering applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hexagons, with accuracy depending on the precision of the input circumradius value.