1. What is a Regular Heptagon?

A regular heptagon is a seven-sided polygon where all sides are equal in length and all angles are equal in measure. Each internal angle measures approximately 128.571 degrees.

2. How Does the Calculator Work?

The calculator uses the heptagon side length formula:

Where:

• \( s \) — Side length
• \( r \) — Radius (distance from center to vertex)
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The formula calculates the side length of a regular heptagon based on its radius (circumradius).

3. Heptagon Properties

Details: A regular heptagon has:

• 7 sides of equal length
• 7 vertices
• Internal angles of ~128.571° each
• Central angles of ~51.4286° each
• Area = \( \frac{7}{4}r^2 \tan\left(\frac{\pi}{7}\right) \)

4. Using the Calculator

Tips: Enter the radius (distance from center to any vertex) in length units. The calculator will compute the side length, perimeter, and area.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radius and apothem?
A: Radius is the distance from center to vertex, while apothem is the distance from center to midpoint of a side.

Q2: Can I calculate the apothem with this?
A: Yes, apothem \( a = r \cos(\pi/7) \), which is about 0.9010 × radius.

Q3: What's the exact value of sin(π/7)?
A: It's approximately 0.43388, but has an exact algebraic expression involving complex roots.

Q4: How precise are the calculations?
A: Results are accurate to 4 decimal places using PHP's trigonometric functions.

Q5: Can this calculator work for irregular heptagons?
A: No, this calculator only works for regular heptagons where all sides and angles are equal.