If there was a lake that occupied $8$ squares, and the width/height of a square was $1km$, it would have an area of $8km^2$. What if the scale was $0.5km$ - the width/height of a square is only $0.5km$, would that mean the area of the lake will be $4km^2$ or $2km^2$?
Area of something on the map when changing the scale
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geometry