1. What is Height of Hexadecagon?

The Height of Hexadecagon is the length of a perpendicular line drawn from one vertex to the opposite side in a regular hexadecagon (16-sided polygon). It represents the maximum vertical distance between parallel sides of the polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Hexadecagon (m)
• \( r_i \) — Inradius of Hexadecagon (m)

Explanation: The height of a regular hexadecagon is exactly twice the length of its inradius, which is the radius of the circle inscribed within the polygon.

3. Importance of Height Calculation

Details: Calculating the height of a hexadecagon is important in various geometric applications, architectural designs, and engineering projects where regular polygonal shapes are used. It helps in determining the overall dimensions and spatial requirements of hexadecagonal structures.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hexadecagon?
A: A regular hexadecagon is a polygon with 16 equal sides and 16 equal angles. All vertices lie on a common circle (circumcircle) and the polygon can be inscribed in a circle.

Q2: How is inradius different from circumradius?
A: Inradius is the radius of the circle inscribed inside the polygon (touching all sides), while circumradius is the radius of the circle that passes through all vertices of the polygon.

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

Q4: What are practical applications of hexadecagons?
A: Hexadecagons are used in architectural designs, mechanical engineering components, decorative patterns, and various geometric constructions where multi-sided symmetry is desired.

Q5: How does the height relate to other hexadecagon measurements?
A: The height is directly proportional to the inradius and can also be related to the side length and circumradius through trigonometric relationships specific to 16-sided polygons.