Circumradius Of Hendecagon Given Area Calculator

Formula Used:

\[ r_c = \frac{\sqrt{\frac{A \times (4 \times \tan(\pi/11))}{11}}}{2 \times \sin(\pi/11)} \]

Circumradius of Hendecagon (r_c):

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1. What is the Circumradius of Hendecagon?

The circumradius of a hendecagon (11-sided polygon) is the radius of a circumcircle that touches all vertices of the hendecagon. It's an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{\sqrt{\frac{A \times (4 \times \tan(\pi/11))}{11}}}{2 \times \sin(\pi/11)} \]

Where:

\( r_c \) — Circumradius of Hendecagon (m)
\( A \) — Area of Hendecagon (m²)
\( \pi \) — Mathematical constant (approximately 3.14159)
\( \tan \) — Tangent trigonometric function
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the circumradius based on the area of the hendecagon using trigonometric relationships specific to an 11-sided polygon.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing and analyzing 11-sided structures, determining spatial relationships, and solving geometric problems involving regular hendecagons.

4. Using the Calculator

Tips: Enter the area of the hendecagon in square meters. The value must be positive and non-zero. The calculator will compute the circumradius based on the input area.

5. Frequently Asked Questions (FAQ)

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

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle passing through all vertices, while inradius is the radius of the circle inscribed within the polygon touching all sides.

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.

Q4: What are practical applications of circumradius calculation?
A: Used in architectural design, mechanical engineering, computer graphics, and any field requiring precise geometric calculations for 11-sided shapes.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and trigonometric functions, providing high accuracy for geometric applications.