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

The formula calculates the side length of a regular dodecagon (12-sided polygon) when its height (distance between opposite sides) is known. This geometric relationship is derived from the properties of regular polygons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side length of the dodecagon (m)
• \( h \) — Height of the dodecagon (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula establishes the mathematical relationship between the height and side length of a regular dodecagon, derived from trigonometric principles and geometric properties.

3. Importance of Side Calculation

Details: Calculating the side length from height is essential in various geometric applications, architectural design, engineering projects, and mathematical problem-solving involving regular dodecagons.

4. Using the Calculator

Tips: Enter the height of the dodecagon in meters. The value must be positive and valid. The calculator will compute the corresponding side length.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the square root of 3 in the formula?
A: The square root of 3 appears due to trigonometric relationships in the 30-60-90 right triangles that can be formed within the dodecagon's structure.

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 used in architectural design, engineering, manufacturing of dodecagonal components, and various mathematical and geometric applications.

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