1. What is an Octagon?

An octagon is an eight-sided polygon with eight angles. A regular octagon has all sides equal and all angles equal (135° each).

2. How Does the Calculator Work?

The calculator uses the octagon side formula:

Where:

• \( s \) — Side length of the octagon
• \( \text{apothem} \) — The apothem (distance from center to midpoint of a side)
• \( \sqrt{2} \) — Approximately 1.41421

Explanation: The formula relates the side length of a regular octagon to its apothem through a constant factor involving √2.

3. Importance of Side Calculation

Details: Calculating the side length is essential for construction, design, and various engineering applications involving octagonal shapes.

4. Using the Calculator

Tips: Enter the apothem measurement in any length unit. The calculator will return the side length in the same units.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between side and apothem?
A: The apothem is always shorter than the side length, specifically about 1.207 times the side length.

Q2: Can I calculate the apothem from the side length?
A: Yes, by rearranging the formula: apothem = side / (2 * (1 + √2)).

Q3: What are common uses of octagons?
A: Octagons are used in architecture (stop signs, building designs), engineering, and various decorative applications.

Q4: How does this relate to the octagon's area?
A: The area of a regular octagon can be calculated as (perimeter × apothem)/2 or 2(1+√2) × side².

Q5: Is this formula only for regular octagons?
A: Yes, this specific formula only applies to regular octagons where all sides and angles are equal.