1. What is the Inradius of Dodecagon?

The inradius of a dodecagon (12-sided polygon) is defined as the radius of the circle which is inscribed inside the dodecagon, touching all its sides. It represents the distance from the center to any side of the dodecagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Dodecagon (m)
• \( h \) — Height of Dodecagon (m)

Explanation: The inradius is calculated as half of the height of the dodecagon, providing a simple relationship between these two geometric properties.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which has applications in various fields including architecture, engineering, and design where regular polygons are used.

4. Using the Calculator

Tips: Enter the height of the dodecagon in meters. The value must be valid (height > 0). The calculator will compute the inradius based on the simple division formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecagon?
A: A dodecagon is a polygon with twelve sides and twelve angles. It is a regular polygon when all sides and angles are equal.

Q2: How is the height of a dodecagon measured?
A: The height of a dodecagon is the perpendicular distance between any pair of opposite sides of the polygon.

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

Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, mechanical engineering, and any field that involves geometric patterns and regular polygons.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular dodecagons and provides precise results when accurate measurements are input.