SOLUTION: On a map with a scale of 1cm:100m, if the area of a field is 180 m2 on the map, what is its actual area in hectares?

Question 1012890: On a map with a scale of 1cm:100m, if the area of a field is 180 m2 on the map, what is its actual area in hectares?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the scale on the map is 1 cm to 100 m.

this means that something with the length of 1 cm on the map is representing something with a length of 100 m in the real world.

i believe you mean that the area is 180 cm^2 on the map.

it's not likely that it will be 180 m^2 on the map because that would be way bigger than the map.

180 square meters is an area that is roughly 13 meters by 13 meters.

it's not likely any representation on the map would be that big.

consequently, i'm going to assume you meant 180 cm^2 on the map.

the scale says that 1 cm on the map is equal to 100 m in the real world.

therefore, an area of 1*1 = 1 square centimeter on the map would be equal to an area of 100*100 = 10,000 square meters in the real world.

180 square cm on the map is therefore equal to 180 * 10,000 = 1,800,000 square meters in the real world.

we can test this out by assuming 180 square centimeters is equal to an area on the map that is 10 cm long by 18 cm wide.

10 cm * 18 cm is equal to 180 square centimeters on the map.

10 cm on the map is equal to 10 * 100 = 1000 meters in the real world.
18 cm on the map is equal to 18 * 100 = 1800 meters in the real world.

this is because the ratio of meters to centimeters is 100 / 1.
therefore, to find equivalent meters in the real world, you multiply the centimeters on the map by 100.

1000 * 1800 is equal to 1,800,000 square meters in the real world.

now we get to hectares.

1 hectare is equal to 10,000 square meters.

divide 1,800,000 by 10,000 and you get 180 hectares.

so 180 square centimeters on the map is equal to 180 hectares in the real world.

that's your solution as best i can determine.

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