A rectangular plot of land measures 30 cm × 40 cm on a cadastral map drawn on a scale of 1 : 5000. Calculate its area in hectares. If a topographical sheet (toposheet) of the area is compiled on a scale of 1 : 50,000, what will be the plot’s area on the toposheet?

Key Information

• Dimensions on Cadastral Map = 30 cm × 40 cm
• Cadastral Map Scale = 1 : 5000
• Toposheet Scale = 1 : 50,000
• Goals: Find the true ground area (in hectares) and the area on the toposheet (in cm²).
• Conversion: 1 hectare = 10,000 m²

Step 1: Calculate Ground Area from Cadastral Map

Step 2: Calculate Area on Toposheet

Final Results

Core Concepts:

1. Map Types & Scales: Different maps serve different purposes and use different scales. Cadastral maps (large scale, e.g., 1:5000) show detailed property boundaries. Topographical maps (smaller scale, e.g., 1:50,000) cover larger areas showing terrain and major features. Larger scale means more detail (1 cm represents less ground).
2. Linear vs. Area Scale: The linear scale relates map distance to ground distance. The area scale (derived by squaring the linear scale factor) relates map area to ground area. This relationship is crucial for area calculations.
3. Area Calculation & Conversion: Calculating area on the map (L×W) and converting it to ground area using the appropriate area scale. Units (cm², m², hectares) must be handled correctly (1 ha = 10,000 m²).
4. Scale Transformation: The same ground area will be represented by different physical areas on maps of different scales. Knowing the ground area allows calculation of its representation on any map if the scale is known.

Real-World Applications:

• Land Administration & Planning: Using detailed cadastral maps for property registration and taxation, and smaller-scale topo maps for regional planning and infrastructure placement.
• Property Development: Assessing site suitability using large-scale cadastral data and understanding the site context using smaller-scale topographical data.
• Environmental Assessment: Calculating specific land parcel areas (cadastral) and relating them to broader environmental features shown on topo maps (e.g., proximity to rivers, forests, elevation contours).
• GIS Integration: Combining data layers from maps of different scales to perform comprehensive spatial analysis for various applications like urban growth studies or resource allocation.
• Agriculture: Managing farm plots using detailed maps and understanding their position within the larger landscape using topographical information.

Why It Works:
The core principle is that the actual ground area of the plot remains constant. The calculation starts with the map providing the most detail (largest scale), the cadastral map (1:5000). The plot’s area on this map (1200 cm²) is converted to the true ground area (3,000,000 m² or 300 hectares) using its specific area scale (1 cm² = 2500 m²). Once this ground truth is established, we can determine how this same area would be represented on a map with a different, smaller scale like the toposheet (1:50,000). The toposheet’s area scale (1 cm² = 250,000 m²) indicates that each square centimeter represents a much larger ground area. Dividing the true ground area by the toposheet’s area scale (3,000,000 m² / 250,000 m²/cm²) gives the smaller area the plot occupies on the toposheet (12 cm²). This demonstrates the inverse relationship between map scale and the physical size of features represented on the map.