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 across 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:

• \( Circumradius \) — The radius of the circumscribed circle that touches all vertices of the nonagon
• \( \pi \) — Mathematical constant approximately equal to 3.14159
• \( \sin \) — Trigonometric sine function

3. Formula Explanation

Details: In a regular nonagon, all sides and angles are equal. The diagonal across four sides can be calculated using trigonometric relationships based on the circumradius and the central angle between vertices (which is 40° or 4π/9 radians between every two vertices).

4. Using the Calculator

Tips: Enter the circumradius of the nonagon in meters. The circumradius must be a positive value greater than zero.

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: How many diagonals does a nonagon have?
A: A nonagon has 27 diagonals in total, with different lengths depending on how many sides they cross.

Q3: What's the relationship between circumradius and side length?
A: In a regular nonagon, side length = 2 × circumradius × sin(π/9).

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

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