Diagonal of Hendecagon across Three Sides given Perimeter Calculator

Formula Used:

\[ Diagonal across Three Sides of Hendecagon = \frac{Perimeter of Hendecagon}{11} \times \frac{\sin\left(\frac{3\pi}{11}\right)}{\sin\left(\frac{\pi}{11}\right)} \]

Diagonal across Three Sides of Hendecagon:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Diagonal across Three Sides of Hendecagon?

A diagonal across three sides of a hendecagon is a straight line joining two non-adjacent vertices that spans across three sides of the 11-sided polygon. It represents one of the longer diagonals in a regular hendecagon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ d_3 = \frac{P}{11} \times \frac{\sin\left(\frac{3\pi}{11}\right)}{\sin\left(\frac{\pi}{11}\right)} \]

Where:

\( d_3 \) — Diagonal across three sides of hendecagon
\( P \) — Perimeter of the hendecagon
\( \pi \) — Mathematical constant pi (approximately 3.14159)
\( \sin \) — Sine trigonometric function

3. Formula Explanation

Details: The formula derives from the geometric properties of regular polygons. The ratio of sine functions accounts for the angular relationships in an 11-sided regular polygon, while dividing the perimeter by 11 gives the side length, which is then scaled by the trigonometric ratio to obtain the diagonal length.

4. Using the Calculator

Tips: Enter the perimeter of the hendecagon in meters. The perimeter must be a positive value. The calculator will compute the diagonal length across three sides based on the mathematical relationship.

5. Frequently Asked Questions (FAQ)

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

Q2: How many diagonals does a hendecagon have?
A: A regular hendecagon has 44 diagonals in total, with different lengths depending on how many sides they span.

Q3: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering design, and any field dealing with regular polygonal structures.

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 is the relationship between side length and this diagonal?
A: For a regular hendecagon, the diagonal across three sides is approximately 2.382 times the side length.