Map Scale Area Calculation

This solution details the calculation of the actual site area in hectares, given its measurement on a map and the map's scale.

Understanding the Map Scale

The provided map scale is 1:16000. This ratio indicates that one unit of distance on the map corresponds to 16000 units of the same distance in reality.

• Map Scale: $1 \text{ : } 16000$
• Length Scale Factor: $16000$

Area Calculation Steps

To find the actual area, the length scale factor must be squared because area is a two-dimensional measurement.

1. Calculate the Area Scale Factor:

   The area scale factor is the square of the length scale factor.

   Area Scale Factor = $(\text{Length Scale Factor})^2 = (16000)^2 = 256,000,000$.

   Therefore, 1 square centimeter (sqcm) on the map represents $256,000,000$ sqcm in the actual area.

2. Calculate Actual Area in Square Centimeters (sqcm):

   Multiply the map area by the area scale factor to find the actual area in sqcm.

   Actual Area (sqcm) = Map Area $\times$ Area Scale Factor

   Actual Area (sqcm) = $75 \text{ sqcm} \times 256,000,000 = 19,200,000,000 \text{ sqcm}$.

3. Convert Actual Area to Square Meters (sqm):

   To convert sqcm to sqm, use the conversion factor $1 \text{ sqm} = 10000 \text{ sqcm}$ (since $1 \text{ m} = 100 \text{ cm}$).

   Actual Area (sqm) = $\frac{19,200,000,000 \text{ sqcm}}{10000 \text{ sqcm/sqm}} = 1,920,000 \text{ sqm}$.

4. Convert Actual Area to Hectares:

   To convert sqm to hectares, use the conversion factor $1 \text{ hectare} = 10000 \text{ sqm}$.

   Actual Area (hectares) = $\frac{1,920,000 \text{ sqm}}{10000 \text{ sqm/hectare}} = 192 \text{ hectares}$.

Final Result

The actual area of the site is 192 hectares.