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

The formula calculates the area of a nonagon (9-sided polygon) when the inradius (radius of the inscribed circle) is known. This formula provides an efficient way to determine the area using the geometric properties of regular nonagons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of Nonagon (m²)
• \( r_i \) — Inradius of Nonagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula utilizes the tangent function to relate the inradius to the area through the geometric properties of the regular nonagon.

3. Importance of Area Calculation

Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. For nonagons, this calculation helps in design applications, material estimation, and spatial planning.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the area using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a nonagon?
A: A nonagon is a nine-sided polygon. When all sides and angles are equal, it's called a regular nonagon.

Q2: What is inradius?
A: Inradius is the radius of the circle inscribed inside the polygon, tangent to all its sides.

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

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, engineering projects, tile patterns, and any application involving nine-sided geometric shapes.

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