1. What is the Area of Hendecagon Formula?

The Area of Hendecagon formula calculates the area of an 11-sided polygon (hendecagon) using the side length. It provides an accurate measurement of the two-dimensional space enclosed by the hendecagon.

2. How Does the Calculator Work?

The calculator uses the Hendecagon area formula:

Where:

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

Explanation: The formula uses trigonometric properties to calculate the area of a regular hendecagon based on its side length.

3. Importance of Area Calculation

Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields for spatial analysis and design purposes.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. When all sides and angles are equal, it's called a regular hendecagon.

Q2: Why use the tangent function in the formula?
A: The tangent function helps calculate the apothem (distance from center to midpoint of a side), which is essential for area calculation of regular polygons.

Q3: Can this formula be used for irregular hendecagons?
A: No, this formula only works for regular hendecagons where all sides and angles are equal. Irregular hendecagons require different calculation methods.

Q4: What are practical applications of hendecagon area calculation?
A: Hendecagon area calculations are used in architectural design, urban planning, manufacturing, and mathematical research involving polygonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hendecagons, with accuracy depending on the precision of the input side length measurement.