Height of Hexadecagon given Area Calculator

Height of Hexadecagon Formula:

\[ h = \sqrt{\frac{A}{4 \cdot \tan\left(\frac{\pi}{16}\right)}} \]

Height of Hexadecagon (h):

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1. What is the Height of Hexadecagon Formula?

The Height of Hexadecagon formula calculates the perpendicular distance from one vertex to the opposite side of a regular hexadecagon (16-sided polygon) when the area is known. This formula is derived from trigonometric relationships in regular polygons.

2. How Does the Calculator Work?

The calculator uses the Height of Hexadecagon formula:

\[ h = \sqrt{\frac{A}{4 \cdot \tan\left(\frac{\pi}{16}\right)}} \]

Where:

\( h \) — Height of Hexadecagon (m)
\( A \) — Area of Hexadecagon (m²)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula derives from dividing the hexadecagon into 16 congruent isosceles triangles and using trigonometric relationships to find the height.

3. Importance of Height Calculation

Details: Calculating the height of a hexadecagon is important in geometry, architectural design, and engineering applications where regular 16-sided polygons are used. It helps in determining spatial dimensions and proportions.

4. Using the Calculator

Tips: Enter the area of the hexadecagon in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding height.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hexadecagon?
A: A regular hexadecagon is a 16-sided polygon where all sides are equal in length and all interior angles are equal (157.5° each).

Q2: Why is the tangent function used in this formula?
A: The tangent function relates the central angle (π/16) to the ratio of opposite and adjacent sides in the right triangles that make up the hexadecagon.

Q3: Can this formula be used for irregular hexadecagons?
A: No, this formula only applies to regular hexadecagons where all sides and angles are equal.

Q4: What are practical applications of hexadecagons?
A: Hexadecagons are used in architecture, mechanical engineering, and design for creating aesthetically pleasing symmetrical shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hexadecagons, though real-world measurements may have practical limitations.