1. What is the Area of Dodecagon Formula?

The area of a regular dodecagon (12-sided polygon) can be calculated using the circumradius with the formula: A = 3 × r_c², where r_c is the circumradius of the dodecagon.

2. How Does the Calculator Work?

The calculator uses the dodecagon area formula:

Where:

• \( A \) — Area of Dodecagon (m²)
• \( r_c \) — Circumradius of Dodecagon (m)

Explanation: This formula provides a direct relationship between the circumradius and the area of a regular dodecagon.

3. Importance of Dodecagon Area Calculation

Details: Calculating the area of geometric shapes like dodecagons is essential in various fields including architecture, engineering, and mathematics education.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular dodecagon?
A: A regular dodecagon is a 12-sided polygon where all sides are equal in length and all interior angles are equal (150° each).

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle that passes through all vertices, while inradius is the radius of the circle inscribed within the polygon.

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

Q4: What are practical applications of dodecagon calculations?
A: Dodecagons are used in architectural designs, clock faces, coin designs, and various decorative patterns.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecagons, with accuracy depending on the precision of the input circumradius value.