1. What is the Diagonal Across Four Sides of Nonagon?

The diagonal across four sides of a nonagon is the straight line joining two non-adjacent vertices which are separated by four sides of the nonagon. It's one of the longer diagonals in a regular nonagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function
• \( \sin \) — Sine trigonometric function
• Inradius of Nonagon — Radius of the circle inscribed inside the nonagon

3. Formula Explanation

Details: This formula derives from the geometric properties of a regular nonagon. The tangent and sine functions relate the inradius to the diagonal length through the internal angles of the nonagon (π/9 and π/18 radians respectively).

4. Using the Calculator

Tips: Enter the inradius of the nonagon in meters. The value must be positive. The calculator will compute the diagonal length across four sides.

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 internal angles are equal (140 degrees each).

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

Q3: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering design, and any field dealing with regular polygonal structures.

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 is the relationship between diagonal length and side length?
A: For a regular nonagon, the diagonal across four sides is approximately 2.879 times the side length.