To find the actual area of a town on the given map, we need to follow a series of steps:
1. Understand the scale of the map: The scale is 1:100000, which means that 1 cm on the map corresponds to 100,000 cm in real life.
2. Determine the area on the map: The area of the town on the map is given as 6 cm².
3. Convert the area from cm² on the map to cm² in real life:
- Since the scale is 1:100000, every linear measurement on the map is 100000 times larger in real life. Therefore, every square measurement (area) is (100000)² times larger in real life.
- Therefore, to find the actual area in cm², multiply the area on the map by 100000²:
[tex]\[
\text{Actual area in cm}^2 = 6 \, \text{cm}^2 \times (100000)^2
\][/tex]
4. Convert the actual area from cm² to m²:
- To convert from cm² to m², we recall that 1 m² = 10000 cm².
[tex]\[
\text{Actual area in m}^2 = \frac{\text{Actual area in cm}^2}{10000}
\][/tex]
5. Convert the actual area from m² to hectares:
- To convert from m² to hectares, we recall that 1 hectare = 10000 m².
[tex]\[
\text{Actual area in hectares} = \frac{\text{Actual area in m}^2}{10000}
\][/tex]
By following these steps, we find the actual area:
1. The map scale is 1:100000.
2. The area on the map is 6 cm².
3. The actual area in cm²:
[tex]\[
6 \, \text{cm}^2 \times (100000)^2 = 6 \times 10000000000 \, \text{cm}^2 = 60000000000 \, \text{cm}^2
\][/tex]
4. The actual area in m²:
[tex]\[
\frac{60000000000 \, \text{cm}^2}{10000} = 6000000 \, \text{m}^2
\][/tex]
5. The actual area in hectares:
[tex]\[
\frac{6000000 \, \text{m}^2}{10000} = 600 \, \text{hectares}
\][/tex]
So, the actual area of the town is 600 hectares.
