Solution: Let the side length of the regular hexagon be $ s $. The distance from the center to a vertex (the radius of the circumscribed circle) is equal to the side length $ s $. Thus, the radius $ R $ of the moat is $ s $. The area of the circle is:
["Discover Sustainable Design: The Hidden Geometry Behind Hexagons in Modern Architecture", "Why are mathematicians suddenly inspiring urban innovation? A growing wave of architects and designers are revisiting the regular hexagon—not just for its beauty, but for its hidden efficiency in space and area calculations. At the heart of this trend lies a simple yet powerful relationship: when the side length of a regular hexagon is $ s $, the distance from the center to any vertex—the radius of the circumscribed circle—is exactly $ s $. This means the circle that perfectly surrounds the hexagon has a radius $ R = s $, and its area can be precisely determined using foundational geometry rules.", "### Is This Geometry Gaining Momentum in the US?", "In cities across the United States, from eco-conscious planner hubs to tech-driven property developers, discussions around hexagonal layouts are increasing. This isn’t a passing fad—it’s rooted in real-world advantages. The regular hexagon’s symmetry supports optimal space utilization, structural balance, and material efficiency. More importantly, its mathematical properties offer predictable, scalable solutions for designers aiming to maximize utility while minimizing waste. As sustainability and precision become core goals in construction and design, understanding such geometric principles is increasingly vital.", "### What Exactly Is the Area of This Hexagonal Moat?", "To calculate the area of a regular hexagon with side length $ s $, architects rely on a clear formula derived from its symmetric structure. Though often associated with decorative patterns and natural forms, the area calculation reveals practical insights. Because each of the six equilateral triangles forming the hexagon has side $ s $, the area is officially:", "$$\n\ ext{Area} = \frac{3\sqrt{3}}{2} s^2\n$$", "This comes from combining six identical equilateral triangles—each with area $ \frac{\sqrt{3}}{4}s^2 $—into one cohesive figure. Though the term “moat” evokes historical design, today’s use in modern planning refers to efficient spatial enclosures, solar panel"]
