A cartographer digitizes aerial maps using rectangles of size 250 m × 250 m per tile. A river basin covers 180 km². How many full tiles are required to cover the entire basin?
["Optimizing Map Analysis: How Many Rectangular Tiles Cover a River Basin?", "In modern cartography, digitizing aerial maps efficiently is essential for geographic information systems (GIS), environmental monitoring, and urban planning. One common approach involves dividing large geographic regions into standardized rectangular tiles to streamline data processing, storage, and visualization.", "### The Standard Grid: 250 m × 250 m Tiles", "Many modern mapping systems use a tiling scheme based on uniform rectangular tiles of fixed dimensions. A popular choice is 250 meters by 250 meters per tile—a resolution ideal for detailed terrain analysis while maintaining manageable data size and computational efficiency. This tile size balances detail and scalability, enabling precise mapping of river basins, forests, or urban footprints.", "---", "### Calculating Area Coverage per Tile", "Each tile covers:", "[\n250, \ ext{m} \ imes 250, \ ext{m} = 62,500, \ ext{square meters} = 0.0625, \ ext{km}^2\n]", "---", "### Total Area to Be Mapped", "The river basin spans 180 km². To determine how many full tiles are required, divide the total area by the area per tile:", "[\n\frac{180, \ ext{km}^2}{0.0625, \ ext{km}^2/\ ext{tile}} = 2,!880, \ ext{tiles}\n]", "---", "### Conclusion: Full Tile Requirement", "Since only full tiles are counted—and rounding up is necessary if partial tiles remain—this calculation depends on how the map boundary aligns with the grid. Assuming optimal alignment, exactly:", "[\n\boxed{2,!880 \ ext{ full } 250, \ ext{m} \ imes 250, \ ext{m} \ ext{ tiles}\n]", "are needed to completely cover the 180 km² river basin using this standardized tiling method.", "This efficient tile-based system enhances GIS workflows, making spatial analysis faster, more scalable, and easier to integrate with remote sensing and environmental modeling tools. Whether for flood risk assessment or watershed management, precise tile sizing ensures reliable and actionable cartographic outputs."]
