SOLUTION: a map has a scale of 1: 50,000 the area of the farm on the map is 6cm^2. What is the real area of the farm in hectares? (1 hectare = 10,000 m^2= 0.01 km^2)

Question 227887: a map has a scale of 1: 50,000
the area of the farm on the map is 6cm^2. What is the real area of the farm in hectares?
(1 hectare = 10,000 m^2= 0.01 km^2)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Scale of the map is 1:50,000

Unless otherwise specified, this is usually a linear measurement.

if it's 1 cm, then real life would be 50,000 cm.

1cm * 1 cm = 1 cm^2 on the map.

50,000 cm * 50,000 cm = 2,500,000,000 cm^2 in real life.

What you would get is 1 cm^2 on the map equals 2,500,000,000 cm^2 in real life.

This means that a farm with an area of 6 cm^2 on the map would be equivalent to a farm with an area of 6*2,500,000,000 cm^2 in real life which would be equal to 15,000,000,000 cm^2 in real life.

Now 1 centimeter = 1/100 of a meter = .01 meter.

1 cm * 1 cm = 1 cm^2

.01 m * .01 m = .0001 m^2

You have 1 cm^2 = .0001 m^2

15,000,000,000 cm^2 * .0001 = 1,500,000 m^2

Since 1 hectare = 10,000 m^2, this means that 1 m^2 = 1/10,000 of a hectare = .0001 hectares.

1,500,000 m^2 * .0001 = 150 hectares.

I believe your answer will be 150 hectares. *****************************

The arithmetic looks good.

If the scale of the map means what I think it does, then these measurements should be good and he area of the farm in hectares should be 150.

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