1. What is the Perimeter of Hexagon given Inradius Formula?

The formula calculates the perimeter of a regular hexagon when its inradius is known. For a regular hexagon, the perimeter can be derived from the inradius using the relationship between the side length and the inradius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Perimeter of Hexagon (m)
• \( r_i \) — Inradius of Hexagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula establishes the relationship between the perimeter of a regular hexagon and its inradius, derived from geometric properties of regular hexagons.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a hexagon is essential in various fields including architecture, engineering, and design. It helps in determining the boundary length for material estimation, construction planning, and spatial analysis.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the perimeter using the mathematical relationship.

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: What is the inradius of a hexagon?
A: The inradius is the radius of the inscribed circle that touches all sides of the hexagon from inside.

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: How is this formula derived?
A: The formula is derived from the relationship between the side length of a regular hexagon and its inradius, multiplied by 6 (number of sides).

Q5: What are practical applications of this calculation?
A: This calculation is used in construction, manufacturing, tessellation patterns, and any application involving hexagonal shapes.