Final answer:
To find the actual area of the forest, multiply the area on the map by the scale factor. Then, convert the area from cm² to km² by dividing by the appropriate conversion factors.
Step-by-step explanation:
To find the actual area of the forest, we need to use the scale factor of the map. The scale factor represents the ratio of the size on the map to the actual size. In this case, the scale factor is 1 : 1,000,000, which means that every 1 cm² on the map represents 1,000,000 cm² in reality.
Since the forest area on the map is 4.6 cm², we can find the actual area by multiplying it with the scale factor:
Actual area = 4.6 cm² x 1,000,000 cm² = 4.6 x 10^6 cm².
However, the question asks for the actual area in square kilometers, so we need to convert cm² to km². There are 10,000 cm² in 1 m², and 1,000 m² in 1 km². Therefore, we can convert cm² to km² by dividing the area in cm² by 10,000 to get the area in m², and then dividing by 1,000,000 to get the area in km².
Actual area = (4.6 x 10^6 cm²) / (10,000 cm²/m²) / (1,000,000 m²/km²) = 0.046 km².