Circumradius of Hendecagon given Diagonal across Two Sides Calculator

Formula Used:

\[ r_c = \frac{d_2}{2 \times \sin\left(\frac{2\pi}{11}\right)} \]

Circumradius of Hendecagon (rₑ):

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1. What is the Circumradius of Hendecagon?

The circumradius of a hendecagon (11-sided polygon) is the radius of a circle that passes through all vertices of the polygon. It's a fundamental geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{d_2}{2 \times \sin\left(\frac{2\pi}{11}\right)} \]

Where:

\( r_c \) — Circumradius of Hendecagon
\( d_2 \) — Diagonal across Two Sides of Hendecagon
\( \pi \) — Mathematical constant pi (approximately 3.14159)
\( \sin \) — Trigonometric sine function

Explanation: This formula calculates the circumradius based on the diagonal measurement across two sides of the hendecagon, using trigonometric relationships specific to the 11-sided polygon.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing and analyzing regular polygons. It helps determine the size and proportions of structures with 11-sided symmetry.

4. Using the Calculator

Tips: Enter the diagonal measurement across two 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 a polygon with 11 sides and 11 angles. It's also known as an undecagon.

Q2: How is this different from the circumradius of other polygons?
A: The formula is specific to hendecagons due to the unique angle (2π/11) used in the sine function, which corresponds to the geometry of an 11-sided polygon.

Q3: Can this calculator be used for irregular hendecagons?
A: No, this calculator is designed specifically for regular hendecagons where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and any field requiring precise geometric measurements of 11-sided structures.

Q5: How accurate is the calculation?
A: The calculation uses PHP's built-in mathematical functions which provide high precision, typically accurate to at least 15 decimal places.