Final answer:
The areal scale corresponding to a linear scale of 4 cm to 100 km is found by squaring both sides of the ratio, leading to a result of 625,000 km² per cm².
Step-by-step explanation:
The areal scale of a map indicates the ratio of a given area on the map to the corresponding area on the ground. The linear scale provided, 4 cm to 100 km, means that 4 cm on the map represents 100 km in reality. To find the areal scale, we square both sides of the linear scale because area is a two-dimensional measurement (length²). Squaring the linear scale ratio, we get:
(4 cm) ² : (100 km) ²
16 cm² : 10,000,000 km²
Therefore, one square centimeter on the map represents 10,000,000/16 square kilometers on the ground, which simplifies to 625,000 km² per cm². This areal scale allows us to understand how areas on a map correspond to real-world areas.