Area of Hexadecagon given Circumradius Calculator

Formula Used:

\[ A = 4 \times \left( \frac{r_c}{\frac{\sqrt{4 + 2\sqrt{2} + \sqrt{20 + 14\sqrt{2}}}}{2}} \right)^2 \times \cot\left(\frac{\pi}{16}\right) \]

Area of Hexadecagon:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Area of Hexadecagon Formula?

The formula calculates the area of a regular hexadecagon (16-sided polygon) given its circumradius. It uses trigonometric functions and square roots to determine the area based on the distance from the center to any vertex.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = 4 \times \left( \frac{r_c}{\frac{\sqrt{4 + 2\sqrt{2} + \sqrt{20 + 14\sqrt{2}}}}{2}} \right)^2 \times \cot\left(\frac{\pi}{16}\right) \]

Where:

\( A \) — Area of Hexadecagon (m²)
\( r_c \) — Circumradius of Hexadecagon (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sqrt{} \) — Square root function
\( \cot \) — Cotangent trigonometric function

Explanation: The formula accounts for the geometric properties of a regular 16-sided polygon, using the circumradius to calculate the area through trigonometric relationships.

3. Importance of Area Calculation

Details: Calculating the area of a hexadecagon is important in geometry, architecture, and design where regular polygons are used. It helps in determining the space occupied by such shapes.

4. Using the Calculator

Tips: Enter the circumradius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a hexadecagon?
A: A hexadecagon is a polygon with 16 sides and 16 angles. When regular, all sides and angles are equal.

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 hexadecagons?
A: No, this formula is specifically for regular hexadecagons where all sides and angles are equal.

Q4: What are practical applications of hexadecagons?
A: Hexadecagons are used in architecture, design, and various engineering applications where symmetrical shapes are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hexadecagons, assuming accurate input values.