Inradius of Hendecagon given Height Calculator

Inradius of Hendecagon given Height Formula:

\[ r_i = \frac{h \cdot \tan(\pi/22)}{\tan(\pi/11)} \]

Inradius of Hendecagon:

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1. What is the Inradius of Hendecagon given Height?

The inradius of a hendecagon (11-sided polygon) is the radius of the circle inscribed within the polygon that is tangent to all its sides. This calculator determines the inradius when the height of the hendecagon is known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{h \cdot \tan(\pi/22)}{\tan(\pi/11)} \]

Where:

\( r_i \) — Inradius of Hendecagon (m)
\( h \) — Height of Hendecagon (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula uses trigonometric relationships derived from the geometry of a regular hendecagon to calculate the inradius based on its height.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various practical applications such as construction, design, and manufacturing where precise measurements of regular polygons are required.

4. Using the Calculator

Tips: Enter the height of the hendecagon in meters. The value must be positive and valid. The calculator will compute the corresponding inradius.

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: What is the relationship between height and inradius?
A: The height and inradius of a regular hendecagon are related through trigonometric functions based on the polygon's internal angles.

Q3: Can this calculator be used for irregular hendecagons?
A: No, this calculator is specifically designed for regular hendecagons where all sides and angles are equal.

Q4: What are the units of measurement?
A: The calculator uses meters for both height and inradius, but the formula works with any consistent unit of length.

Q5: Are there limitations to this calculation?
A: This calculation assumes a perfect regular hendecagon and uses mathematical constants with finite precision, though the error is negligible for most practical purposes.