Given that the area of a forest on the map is 6 cm^2, calculate the actual area of the forest in square kilometers. The scale of the map is 1 cm : 2.5 km.
This question can be answered by setting up a proportion. But first, we need to understand how to convert the area of the region on the map to the area of the land this region represents.
If the scale of the map is 1 cm : 2.5 km, this means that 1 cm on the map corresponds to the 2.5 km of the actual land. The square on the map that has a side of 1 cm has the area of `1 cm * 1 cm` , or 1 square cm. Then, this square of the map corresponds to the piece of the actual land that has the area of
`2.5 km * 2.5 km = 6.25` square km.
Therefore the proportion we need to answer the question is
1 square cm corresponds to 6.25 square km
6 sq. cm (area of the forest on the map) corresponds to unknown area of the actual forest, x sq. km.
This can be written as the equality of two ratios:
`1/6.25 = 6/x`
Alternatively, it can also be written as `1/6 = 6.25/x` .
In any case, the proportion can be solved by cross-multiplying:
1*x = 6*6.25
x = 37.5 square km.
The actual area of the forest represented by 6 sq. cm region on the map is 37.5 square kilometers.