Area of Hendecagon given Circumradius Calculator

Formula Used:

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

Area of Hendecagon:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Area of Hendecagon given Circumradius?

The area of a hendecagon (11-sided polygon) given its circumradius is calculated using a specific mathematical formula that relates the circumradius to the area of the polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the area of a regular hendecagon based on its circumradius using trigonometric relationships.

3. Importance of Area Calculation

Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields for design, analysis, and problem-solving purposes.

4. Using the Calculator

Tips: Enter the circumradius value 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 is also known as an undecagon.

Q2: What is circumradius?
A: Circumradius is the radius of a circle that passes through all the vertices of a 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.

Q4: What are the practical applications of this calculation?
A: This calculation is used in architectural design, engineering projects, and mathematical modeling where regular hendecagonal shapes are involved.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and trigonometric functions, providing highly accurate results for the given inputs.