1. What is the Area of Hexagon given Inradius?

The area of a regular hexagon can be calculated using its inradius (the radius of the inscribed circle). This formula provides a direct relationship between the inradius and the area of the hexagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of Hexagon (m²)
• \( r_i \) — Inradius of Hexagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula derives from the geometric properties of a regular hexagon, where the inradius relates to the side length and ultimately to the area.

3. Importance of Area Calculation

Details: Calculating the area of a hexagon is important in various fields including architecture, engineering, and design where hexagonal shapes are commonly used for their structural efficiency and aesthetic appeal.

4. Using the Calculator

Tips: Enter the inradius value in 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 inradius related to side length?
A: For a regular hexagon, the inradius \( r_i = \frac{\sqrt{3}}{2} \times a \), where \( a \) is the side length.

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 hexagonal shapes?
A: Hexagonal shapes are used in honeycomb structures, bolt heads, floor tiles, and various engineering applications due to their efficient packing and structural strength.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexagons, provided the input inradius is accurate.