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

The formula calculates the width of a regular octagon based on its inradius. The width is defined as the horizontal distance from the leftmost edge to the rightmost edge of the regular octagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( w \) — Width of Octagon (m)
• \( r_i \) — Inradius of Octagon (m)

Explanation: The width of a regular octagon is exactly twice the length of its inradius. This relationship holds true for all regular octagons.

3. Importance of Width Calculation

Details: Calculating the width of an octagon is essential in various geometric applications, architectural designs, and engineering projects where octagonal shapes are used.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be a positive number greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octagon?
A: A regular octagon is an eight-sided polygon where all sides are equal in length and all angles are equal in measure.

Q2: What is the inradius of an octagon?
A: The inradius is the radius of the incircle of the regular octagon, which is the circle that touches all eight sides of the octagon.

Q3: Are there other ways to calculate octagon width?
A: Yes, the width can also be calculated using side length or circumradius, but the inradius method provides a direct relationship.

Q4: What are common applications of octagonal shapes?
A: Octagons are commonly used in architecture (stop signs, building designs), engineering, and various decorative patterns.

Q5: Does this formula work for irregular octagons?
A: No, this formula only applies to regular octagons where all sides and angles are equal.