1. What is the Inradius of Octagon?

The inradius of a regular octagon is the radius of the inscribed circle that touches all eight sides of the octagon. It represents the distance from the center of the octagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the inradius formula:

Where:

• \( r_i \) — Inradius of the octagon (m)
• \( A \) — Area of the octagon (m²)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the inradius based on the area of a regular octagon, using the mathematical relationship between the area and the inscribed circle's radius.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and engineering applications where the relationship between an octagon and its inscribed circle needs to be determined, such as in mechanical design and architectural planning.

4. Using the Calculator

Tips: Enter the area of the octagon in square meters. The value must be positive and greater than zero for accurate calculation.

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 interior angles are equal (135 degrees each).

Q2: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching the sides), while the circumradius is the radius of the circumscribed circle (passing through the vertices).

Q3: Can this formula be used for irregular octagons?
A: No, this formula applies only to regular octagons where all sides and angles are equal.

Q4: What are practical applications of octagon inradius calculation?
A: Applications include architectural design, mechanical engineering, manufacturing of octagonal components, and geometric modeling.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octagons, provided the input area is accurate.