1. What is the Side of Dodecagon Given Area Formula?

The formula calculates the side length of a regular dodecagon (12-sided polygon) when its area is known. This geometric relationship allows for precise dimensioning of the polygon based on its surface area.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side length of the dodecagon (m)
• \( A \) — Area of the dodecagon (m²)

Explanation: The formula derives from the geometric properties of a regular dodecagon, where the area can be expressed in terms of the side length and the mathematical constant √3.

3. Importance of Side Length Calculation

Details: Calculating the side length from area is essential in geometry, architecture, and design applications where dodecagonal shapes are used. It helps in material estimation, structural planning, and spatial arrangement.

4. Using the Calculator

Tips: Enter the area of the dodecagon in square meters. The value must be positive and greater than zero for valid 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: Why is √3 used in the formula?
A: The √3 constant appears due to the trigonometric relationships in the dodecagon's geometry, specifically from the 30-60-90 triangle properties within the shape.

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 dodecagons?
A: Dodecagons are used in architecture, coin design (some countries), clock faces, and various decorative patterns.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecagons, though practical measurements may have slight variations.