1. What is the Perimeter of Hendecagon given Area Formula?

The formula calculates the perimeter of a regular hendecagon (11-sided polygon) when its area is known. It provides a mathematical relationship between the area and perimeter of a regular hendecagon.

2. How Does the Calculator Work?

The calculator uses the perimeter formula:

Where:

• \( P \) — Perimeter of Hendecagon (m)
• \( A \) — Area of Hendecagon (m²)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula derives from the geometric properties of regular polygons, using trigonometric functions to relate area to perimeter.

3. Importance of Perimeter Calculation

Details: Calculating perimeter from area is essential in various geometric applications, architectural design, and engineering projects involving regular hendecagons.

4. Using the Calculator

Tips: Enter the area of the hendecagon in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hendecagon?
A: A regular hendecagon is an 11-sided polygon where all sides are equal in length and all interior angles are equal.

Q2: Why use the tangent function in this formula?
A: The tangent function helps relate the area to the side length through the central angle of the polygon (π/11 radians).

Q3: Can this formula be used for irregular hendecagons?
A: No, this formula only applies to regular hendecagons 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 mathematical geometry problems involving regular 11-sided figures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hendecagons, though computational precision depends on the implementation.