Height of Hendecagon given Perimeter Calculator

Formula Used:

\[ h = \frac{P}{22 \cdot \tan\left(\frac{\pi}{22}\right)} \]

Height of Hendecagon (h):

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1. What is the Height of Hendecagon given Perimeter?

The height of a hendecagon (11-sided polygon) is the perpendicular distance from one side to the opposite vertex. This calculator determines the height when the perimeter is known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{P}{22 \cdot \tan\left(\frac{\pi}{22}\right)} \]

Where:

\( h \) — Height of Hendecagon (m)
\( P \) — Perimeter 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, using trigonometric relationships between the perimeter and height.

3. Importance of Height Calculation

Details: Calculating the height of a hendecagon is important in geometry, architecture, and design where regular polygons are used. It helps in determining the spatial dimensions and proportions of the shape.

4. Using the Calculator

Tips: Enter the perimeter of the hendecagon in meters. The value must be positive and greater than zero.

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 is called a regular hendecagon.

Q2: Why is the tangent function used in the formula?
A: The tangent function relates the angle at the center of the polygon to the ratio of the side length to the height, which is essential for calculating the height from the perimeter.

Q3: Can this formula be used for irregular hendecagons?
A: No, this formula is specifically for regular hendecagons where all sides and angles are equal. Irregular hendecagons require different methods for height calculation.

Q4: What are practical applications of this calculation?
A: This calculation is useful in fields like architecture, engineering, and design where regular polygons are used in structures, patterns, and artistic designs.

Q5: How accurate is the calculated height?
A: The accuracy depends on the precision of the input perimeter value and the mathematical constants used. The calculator provides results with high precision.