1. What is the Perimeter of Dodecagon given Inradius?

The perimeter of a dodecagon (12-sided polygon) can be calculated from its inradius using the formula: \( P = \frac{12 \times r_i}{\frac{2 + \sqrt{3}}{2}} \), where \( r_i \) is the inradius of the dodecagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula relates the perimeter of a regular dodecagon to its inradius through geometric relationships specific to 12-sided regular polygons.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of geometric shapes is fundamental in various fields including architecture, engineering, and mathematics. For regular polygons like dodecagons, knowing the inradius allows for quick determination of the perimeter.

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 dodecagon?
A: A dodecagon is a polygon with twelve sides and twelve angles. When all sides and angles are equal, it is called a regular dodecagon.

Q2: What is the inradius of a polygon?
A: The inradius is the radius of the inscribed circle (incircle) of the polygon, which touches all sides of the polygon from the inside.

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

Q4: What are practical applications of dodecagon perimeter calculations?
A: Dodecagons are used in various designs including architectural elements, coin shapes, and mechanical parts where their symmetrical properties are advantageous.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecagons, though practical measurements of inradius may introduce some error.