1. What is the Height of Nonagon Given Inradius Formula?

The formula calculates the height of a regular nonagon (9-sided polygon) given its inradius. The inradius is the radius of the circle inscribed within the nonagon that touches all its sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Nonagon (m)
• \( r_i \) — Inradius of Nonagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sec \) — Secant trigonometric function

Explanation: The formula derives from the geometric properties of a regular nonagon, where the height can be expressed in terms of the inradius using trigonometric relationships.

3. Importance of Height Calculation

Details: Calculating the height of a nonagon is important in various geometric applications, architectural design, and engineering projects involving polygonal structures.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a regular nonagon?
A: A regular nonagon is a nine-sided polygon where all sides are equal in length and all interior angles are equal (140° each).

Q2: What is the inradius of a polygon?
A: The inradius is the radius of the inscribed circle that touches all sides of the polygon from the inside.

Q3: How accurate is this formula?
A: The formula is mathematically exact for regular nonagons and provides precise results when correct input values are used.

Q4: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.

Q5: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering design, computer graphics, and any field dealing with geometric modeling of polygonal shapes.