Circumradius of Hendecagon given Perimeter Calculator

Circumradius of Hendecagon Formula:

\[ r_c = \frac{P}{22 \times \sin(\pi/11)} \]

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 that helps in understanding the spatial dimensions of an 11-sided polygon.

2. How Does the Calculator Work?

The calculator uses the Circumradius of Hendecagon formula:

\[ r_c = \frac{P}{22 \times \sin(\pi/11)} \]

Where:

\( r_c \) — Circumradius of Hendecagon (m)
\( P \) — Perimeter of Hendecagon (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the circumradius by dividing the perimeter by 22 times the sine of π/11, which is derived from the geometric properties of a regular hendecagon.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry for determining the size of the circumscribed circle around a hendecagon, which has applications in various fields including architecture, engineering, and design.

4. Using the Calculator

Tips: Enter the perimeter 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 geometric shape with eleven edges and eleven vertices.

Q2: Why is the sine function used in the formula?
A: The sine function is used to relate the central angle of the hendecagon to its side length, which is essential for calculating the circumradius in a regular polygon.

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 circumradius calculation.

Q4: What are the units for the circumradius?
A: The circumradius is measured in meters (m), consistent with the perimeter input. Ensure consistent units for accurate results.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hendecagons, using the constant π and trigonometric functions with high precision.