Illustrate a regular octagon of side length 6 cm with 135° interior angles

Here is an illustration of a regular octagon with a side length of 6 cm and interior angles of 135°. The octagon is inscribed in a circle, which ensures all sides and angles are equal.

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Here are 8 questions related to this illustration:
1. How do you calculate the radius of the circumscribed circle for a regular octagon?
2. What is the relationship between the side length and the radius of a regular polygon?
3. How can you derive the interior angle of a regular octagon?
4. What are the properties of a regular octagon?
5. How does the number of sides affect the shape of a regular polygon?
6. Can you explain the process of plotting a regular octagon using trigonometric functions?
7. How would the shape change if the side length were doubled?
8. What other types of polygons can be inscribed in a circle similarly?

**Tip:** In regular polygons, each interior angle can be calculated using the formula \(\frac{(n-2) \times 180°}{n}\), where \(n\) is the number of sides.

Explore how to illustrate a regular octagon with 135° interior angles, featuring a side length of 6 cm. Understand the geometric properties of regular polygons, including formulas for interior angles and relationships between side lengths and circumscribed circles. Suitable for high school students in Grades 10-12.

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