1. What is Height of Dodecagon given Circumradius?

The Height of a Dodecagon given its Circumradius is the vertical distance between two opposite sides of the regular twelve-sided polygon, calculated based on the radius of its circumscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_c \) — Circumradius of the Dodecagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• \( \sqrt{6} \) — Square root of 6 (approximately 2.449)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula derives from the geometric properties of a regular dodecagon and its relationship with its circumscribed circle.

3. Importance of Height Calculation

Details: Calculating the height of a dodecagon is essential in various geometric applications, architectural designs, and engineering projects involving twelve-sided structures.

4. Using the Calculator

Tips: Enter the circumradius 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 regular, all sides and angles are equal.

Q2: What is Circumradius?
A: Circumradius is the radius of a circle that passes through all vertices of a polygon.

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

Q4: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering design, and various geometric computations involving dodecagonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular dodecagons, though real-world measurements may introduce minor variations.