1. What is Diagonal Across Three Sides of Dodecagon?

A diagonal across three sides of a dodecagon is a straight line joining two non-adjacent vertices that spans across three sides of the twelve-sided polygon. It represents one of the longer diagonals in a regular dodecagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{2} \) — Square root of 2 (approximately 1.414214)
• \( Circumradius \) — Radius of the circumscribed circle that passes through all vertices of the dodecagon

3. Formula Explanation

Details: This formula derives from the geometric properties of a regular dodecagon. The square root of 2 factor comes from the relationship between the circumradius and the diagonal measurements in this specific polygon configuration.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The circumradius must be a positive number greater than zero. The calculator will compute the diagonal length across three sides of the dodecagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecagon?
A: A dodecagon is a twelve-sided polygon with twelve angles and twelve vertices.

Q2: How many diagonals does a dodecagon have?
A: A dodecagon has 54 diagonals in total, with different lengths depending on how many sides they span.

Q3: What is the circumradius of a polygon?
A: The circumradius is the radius of the circumscribed circle that passes through all vertices of the polygon.

Q4: Can this formula be used for irregular dodecagons?
A: No, this formula applies only to regular dodecagons where all sides and angles are equal.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering design, and any field dealing with regular polygonal structures.