a scale distance of 3.5 cm on a certain maps represents an actual 17.5 km.what actual area does 7 square centimetres on the dame map represents?
To determine the actual area represented by 7 square centimeters on the same map, we need to first find the scale factor between the map's distance and the actual distance.
Given that a scale distance of 3.5 cm represents an actual distance of 17.5 km, we can calculate the scale factor by dividing the actual distance by the scale distance:
Scale factor = Actual distance / Scale distance
Scale factor = 17.5 km / 3.5 cm
Now we can use the scale factor to find the scale area. Since area is measured in square units, we'll need to square the scale factor:
Scale area = Scale factor^2
Let's calculate the scale factor and scale area:
Scale factor = 17.5 km / 3.5 cm = 5 km/cm
Scale area = (5 km/cm)^2 = 25 km^2/cm^2
Now, to find the actual area, we multiply the scale area by the given 7 square centimeters:
Actual area = Scale area * Given area
Actual area = 25 km^2/cm^2 * 7 cm^2
When multiplying the units, the square centimeters cancel out, leaving us with the final answer in square kilometers:
Actual area = 25 km^2/cm^2 * 7 cm^2 = 175 km^2
Therefore, 7 square centimeters on the same map represents an actual area of 175 square kilometers.
just use a proportion to first find the length.
3.5cm/17.5km = 7cm/x km
3.5x = 7(17.5)
x = 35
so 7 cm represents 35 km
the area of that would be 35^2 = 1225 km^2