1. What is the Width of Heptagon given Inradius Formula?

The formula calculates the width of a regular heptagon based on its inradius. It utilizes trigonometric functions to establish the relationship between the inradius and the width of the heptagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( w \) — Width of Heptagon (m)
• \( r_i \) — Inradius of Heptagon (m)
• \( \pi \) — Archimedes' constant (≈3.14159)
• \( \tan \) — Tangent trigonometric function
• \( \sin \) — Sine trigonometric function

Explanation: The formula derives from the geometric properties of a regular heptagon, using trigonometric relationships between the inradius and the width.

3. Importance of Width Calculation

Details: Calculating the width of a heptagon is essential in various geometric and architectural applications, helping in design and spatial planning where heptagonal shapes are involved.

4. Using the Calculator

Tips: Enter the inradius of the heptagon 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 with all sides and angles equal.

Q2: How is the inradius defined for a heptagon?
A: The inradius is the radius of the circle inscribed inside the heptagon, touching all its sides.

Q3: Can this formula be used for irregular heptagons?
A: No, this formula is specifically for regular heptagons where all sides and angles are equal.

Q4: What are the units for the inputs and outputs?
A: Both the inradius and the calculated width are in meters. Ensure consistent units for accurate results.

Q5: Why are trigonometric functions used in this formula?
A: Trigonometric functions help relate the inradius to the width through the angles inherent in the heptagon's structure.