1. What is the Area of Hendecagon Formula?

The formula calculates the area of a regular hendecagon (11-sided polygon) given its inradius. The inradius is the radius of the circle inscribed within the hendecagon that touches all its sides.

2. How Does the Calculator Work?

The calculator uses the hendecagon area formula:

Where:

• \( A \) — Area of the hendecagon
• \( \pi \) — Mathematical constant (approximately 3.14159)
• \( r_i \) — Inradius of the hendecagon
• \( \tan \) — Tangent trigonometric function

Explanation: The formula derives from dividing the hendecagon into 11 congruent isosceles triangles and calculating their total area using trigonometric relationships.

3. Importance of Area Calculation

Details: Calculating the area of regular polygons is fundamental in geometry and has applications in various fields including architecture, engineering, and design where precise area measurements are required.

4. Using the Calculator

Tips: Enter the inradius value in meters. The inradius must be a positive number greater than zero. The calculator will compute the area in square meters.

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: What is the inradius of a polygon?
A: The inradius is the radius of the inscribed circle that touches all sides of the polygon from inside.

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.

Q4: What are practical applications of hendecagon area calculation?
A: Hendecagons are used in architectural design, coin design (some countries), and various decorative patterns where symmetrical 11-sided shapes are desired.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hendecagons, though practical measurements may have slight variations due to manufacturing tolerances.