Inradius of Hendecagon given Diagonal across Two Sides Calculator

Formula Used:

\[ Inradius = \frac{\left(\frac{Diagonal \times \sin(\pi/11)}{\sin(2\pi/11)}\right)}{2 \times \tan(\pi/11)} \]

Inradius of Hendecagon:

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1. What is the Inradius of Hendecagon?

The inradius of a hendecagon (11-sided polygon) is the radius of the circle that fits perfectly inside the hendecagon, touching all its sides. It represents the distance from the center to any side of the polygon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Inradius = \frac{\left(\frac{Diagonal \times \sin(\pi/11)}{\sin(2\pi/11)}\right)}{2 \times \tan(\pi/11)} \]

Where:

\( Diagonal \) — Diagonal across two sides of the hendecagon (meters)
\( \pi \) — Mathematical constant approximately equal to 3.14159
\( \sin \) — Sine trigonometric function
\( \tan \) — Tangent trigonometric function

Explanation: This formula calculates the inradius based on the diagonal measurement across two sides, using trigonometric relationships specific to an 11-sided polygon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which has applications in various fields including architecture, engineering, and design where regular polygons are used.

4. Using the Calculator

Tips: Enter the diagonal measurement across two sides of the hendecagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. It is also known as an undecagon.

Q2: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching all sides), while the circumradius is the radius of the circumscribed circle (passing through all vertices).

Q3: Can this formula be used for other polygons?
A: No, this specific formula is designed for hendecagons (11-sided polygons). Other polygons have different formulas based on their number of sides.

Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, mechanical engineering, and geometric modeling where regular hendecagonal shapes are used.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input value, using the exact trigonometric relationships for a regular hendecagon.