Inradius Of Hendecagon Given Diagonal Across Five Sides Calculator

Formula Used:

\[ Inradius = \frac{\left(\frac{Diagonal \times \sin(\pi/11)}{\sin(5\pi/11)}\right)}{2 \times \tan(\pi/11)} \]

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's an important geometric property that helps in various calculations related to the polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Inradius = \frac{\left(\frac{Diagonal \times \sin(\pi/11)}{\sin(5\pi/11)}\right)}{2 \times \tan(\pi/11)} \]

Where:

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

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

3. Importance of Inradius Calculation

Details: The inradius is crucial for determining the area of the hendecagon, understanding its geometric properties, and for various applications in architecture, engineering, and design where regular polygons are used.

4. Using the Calculator

Tips: Enter the diagonal measurement across five sides 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 an 11-sided polygon with equal sides and angles, making it a regular polygon.

Q2: How is the diagonal across five sides measured?
A: It's the straight line distance between two non-adjacent vertices with four vertices between them in the hendecagon.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometric design, architectural planning, and mathematical research involving regular polygons.

Q4: Can this formula be used for irregular hendecagons?
A: No, this formula specifically applies to regular hendecagons where all sides and angles are equal.

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