Height Of Hendecagon Given Inradius Calculator

Formula Used:

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

Height of Hendecagon (h):

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1. What is the Height of Hendecagon given Inradius Formula?

The formula calculates the height of a regular hendecagon (11-sided polygon) when its inradius (radius of inscribed circle) is known. It uses trigonometric relationships involving the tangent function.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula derives from the geometric properties of a regular hendecagon and the trigonometric relationships between its inradius and height.

3. Importance of Height Calculation

Details: Calculating the height of a hendecagon is important in geometry, architecture, and various engineering applications where regular polygons are used. It helps in determining the overall dimensions and proportions of hendecagonal structures.

4. Using the Calculator

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

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 inradius of a polygon?
A: The inradius is the radius of the circle that can be inscribed inside the polygon, touching all its sides.

Q3: Why use tangent functions in this formula?
A: Tangent functions help relate the angles at the center of the polygon to the distances from the center to the sides and vertices.

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

Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, mechanical engineering, and any field that involves geometric modeling of 11-sided structures.