Circumradius Of Hendecagon Given Diagonal Across Three Sides Calculator

Formula Used:

\[ r_c = \frac{d_3}{2 \times \sin\left(\frac{3\pi}{11}\right)} \]

Circumradius of Hendecagon (r_c):

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1. What is the Circumradius of Hendecagon?

The Circumradius of Hendecagon is the radius of a circumcircle touching each of the vertices of Hendecagon. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{d_3}{2 \times \sin\left(\frac{3\pi}{11}\right)} \]

Where:

\( r_c \) — Circumradius of Hendecagon (m)
\( d_3 \) — Diagonal across Three Sides of Hendecagon (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: This formula calculates the circumradius based on the diagonal measurement across three sides of a regular hendecagon, using trigonometric relationships inherent in the polygon's geometry.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential for understanding the geometric properties of hendecagons, designing polygonal structures, and solving complex geometric problems involving regular polygons.

4. Using the Calculator

Tips: Enter the diagonal measurement across three sides of the hendecagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is an 11-sided polygon, also known as an undecagon. It is a regular polygon when all sides and angles are equal.

Q2: How is the diagonal across three sides measured?
A: The diagonal across three sides connects two non-adjacent vertices with exactly two vertices between them along the polygon's perimeter.

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 circumradius calculation?
A: Circumradius calculations are used in architecture, engineering design, computer graphics, and various mathematical modeling applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hendecagons, though practical measurements may introduce some error.