Perimeter of Hendecagon given Diagonal across Two Sides Calculator

Formula Used:

\[ P = 11 \times \frac{d_2 \times \sin(\pi/11)}{\sin(2\pi/11)} \]

Perimeter of Hendecagon:

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1. What is Perimeter of Hendecagon given Diagonal across Two Sides?

The perimeter of a hendecagon (11-sided polygon) given the diagonal across two sides is the total length around the hendecagon, calculated using the diagonal measurement between two non-adjacent vertices separated by one vertex.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 11 \times \frac{d_2 \times \sin(\pi/11)}{\sin(2\pi/11)} \]

Where:

\( P \) — Perimeter of Hendecagon (m)
\( d_2 \) — Diagonal across Two Sides of Hendecagon (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: This formula derives from the geometric properties of a regular hendecagon and trigonometric relationships between sides and diagonals.

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, structural design, and spatial planning.

4. Using the Calculator

Tips: Enter the diagonal across two sides measurement in meters. The value must be positive and greater than zero. The calculator will compute the corresponding perimeter of the regular 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 is called a regular hendecagon.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular hendecagon. Real-world measurements may have slight variations due to measurement precision.

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

Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, manufacturing of polygonal components, and mathematical problem solving involving regular polygons.

Q5: How is the diagonal across two sides measured?
A: The diagonal across two sides is the straight line distance between two non-adjacent vertices with exactly one vertex between them in a regular hendecagon.