1. What is Long Diagonal of Heptagon?

The Long Diagonal of a Heptagon is the straight line joining two non-adjacent vertices which is across three sides of the Heptagon. It is one of the important geometric properties of a regular heptagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function
• Circumradius — Radius of the circumcircle touching each vertex of the heptagon

Explanation: This formula calculates the long diagonal length based on the circumradius of a regular heptagon using trigonometric relationships.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is important in geometry and various practical applications involving heptagonal shapes, including architectural design, engineering, and mathematical analysis.

4. Using the Calculator

Tips: Enter the circumradius 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 heptagon?
A: A regular heptagon is a seven-sided polygon where all sides are equal in length and all interior angles are equal.

Q2: How is the circumradius related to the heptagon?
A: The circumradius is the distance from the center of the heptagon to any of its vertices.

Q3: What are the practical applications of this calculation?
A: This calculation is useful in geometry problems, architectural design involving heptagonal structures, and various engineering applications.

Q4: Can this formula be used for irregular heptagons?
A: No, this formula is specifically for regular heptagons where all sides and angles are equal.

Q5: What is the difference between long and short diagonals?
A: In a heptagon, the long diagonal spans three sides while shorter diagonals span one or two sides.