Perimeter of Hendecagon given Height Calculator

Hendecagon Perimeter Formula:

\[ P = 22 \times h \times \tan(\pi/22) \]

Perimeter of Hendecagon (P):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The formula calculates the perimeter of a regular hendecagon (11-sided polygon) when the height (distance from center to midpoint of a side) is known. This geometric relationship uses trigonometric functions to derive the side length from the height.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 22 \times h \times \tan(\pi/22) \]

Where:

\( P \) — Perimeter of Hendecagon (m)
\( h \) — Height of Hendecagon (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula derives from the geometric properties of a regular hendecagon, using the tangent function to relate the height to the side length, then multiplying by 11 to get the total perimeter.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of geometric shapes is fundamental in various fields including architecture, engineering, and mathematics. For regular polygons like hendecagons, perimeter calculations help in material estimation, construction planning, and geometric analysis.

4. Using the Calculator

Tips: Enter the height of the hendecagon in meters. The height must be a positive value greater than zero. The calculator will compute the corresponding perimeter using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is an 11-sided polygon. When all sides and angles are equal, it's called a regular hendecagon.

Q2: Why use the tangent function in this formula?
A: The tangent function relates the height (apothem) to half the side length through the central angle of the polygon, which is π/11 radians for a hendecagon.

Q3: Can this formula be used for irregular hendecagons?
A: No, this formula only applies to regular hendecagons where all sides and angles are equal. Irregular hendecagons require summing individual side lengths.

Q4: What are practical applications of hendecagon perimeter calculations?
A: Hendecagons are used in architectural design, coin minting (some countries have 11-sided coins), and various decorative patterns where symmetry is desired.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular hendecagons. The accuracy depends on the precision of the input height value and the implementation of the tangent function.