1. What is the Inradius of Hexagon given Perimeter?

The inradius of a hexagon is the radius of the incircle that fits perfectly inside the hexagon, touching all its sides. Given the perimeter, we can calculate the inradius using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Hexagon (m)
• \( P \) — Perimeter 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 relationship between perimeter and inradius is fixed.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in various geometric and engineering applications, including determining the size of inscribed circles and optimizing space within hexagonal structures.

4. Using the Calculator

Tips: Enter the perimeter of the hexagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hexagon?
A: A regular hexagon is a six-sided polygon with all sides of equal length and all internal angles equal to 120 degrees.

Q2: How is the inradius related to the side length?
A: For a regular hexagon, the inradius can also be expressed as \( r_i = \frac{s\sqrt{3}}{2} \), where s 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 this calculation?
A: This calculation is useful in fields like architecture, engineering, and design where hexagonal patterns are used.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexagons, provided accurate input values are given.