Area of Hendecagon given Perimeter Calculator

Formula Used:

\[ A = \frac{P^2}{44 \cdot \tan(\pi/11)} \]

Area of Hendecagon:

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

The formula calculates the area of a regular hendecagon (11-sided polygon) when its perimeter is known. It provides an accurate measurement of the two-dimensional space enclosed by the hendecagon.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{P^2}{44 \cdot \tan(\pi/11)} \]

Where:

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

Explanation: The formula derives from the geometric properties of regular polygons and uses trigonometric functions to calculate the area based on the perimeter.

3. Importance of Area Calculation

Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. For regular polygons like hendecagons, area calculation helps in material estimation, space planning, and structural design.

4. Using the Calculator

Tips: Enter the perimeter of the hendecagon in meters. The value must be positive and greater than zero. The calculator will compute the area using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with eleven sides and eleven 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 relate the side length to the apothem (distance from center to midpoint of a side), which is essential for area calculation in 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 methods for area calculation.

Q4: What are practical applications of hendecagon area calculation?
A: Hendecagons are used in architecture, design, and various engineering applications where unique geometric shapes are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hendecagons. The accuracy depends on the precision of the input perimeter value.