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Question 1016731: The scale of a map is 1:20 000. Find the area on the map which represents 124km squared.
Thanks so much! How do you do this?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it's important to know what the measurements are on the map versus what the measurements are in the real world.
you are told that the area is 124 square kilometers in real life.
the scale on the map says 1 something on the map is equal to 20,000 somethings in real life.
it's probably a centimeter on the map is equal to 20,000 meters in real life, although that's just a guess.
assuming the guess is correct, you would find the area on the map in the following manner.
20,000 meters is equal to 20 kilometers.
that means that 1 centimeter on the map is equal to 20 kilometers in real life.
that's a linear measurement.
the area on the map would be 1 * 1 = 1 square meter.
the corresponding area in the real world would be 20 * 20 = 400 square kilometers.
the scale on the map can therefore be translated as follows:
1 centimeter on the map equals 20 kilometers in the real world.
1 square centimeter on the map equals 400 square kilometers in the real world.
your real world measurements are 124 square kilometers.
your translation factors is 1 / 400 = x / 124
that says that 1 square centimeter on the map divided by 400 square kilometers in the real world is the same ratio as 2 square centimeters on the map divided by 124 square kilometers in the real world.
you would cross multiply to get 1 * 124 = 400 * x
you would solve for x to get x = (1 * 124) / 400 = .31 square centimeters on the map.
this says that .31 square centimeters on the map is equal to 124 square kilometers in the real world.
if you give your area in the world world some dimensions, this might be easier to see.
assume that 124 square kilometers is a strip of land 10 kilometers by 12.4 kilometers in the real world.
10 * 12.4 = 124 square kilometers.
the scale on the map is 1:20,000 which we have assumed is 1 centimeter to 20,000 meters, which we have translated to 1 centimeter to 20 kilometers.
the area in the real world is 10 kilometers by 12.4 kilometers.
the scale on the map says 1 centimeter on the map is equal to 20 kilometers in the real world.
a scale of 1:20 means that the measurement on the map is 1/20 * the measurement in the real world, and the measurement on the map is centimeters while the measurement in the real world is kilometers.
a distance of 10 kilometers in the real world is therefore equal to 1/20 * 10 = .5 centimeters on the map.
a distance of 12.4 kilometers in the real world is therefore equal to 1/20 * 12.4 = .62 centimeters on the map.
the dimensions in the real world are 10 kilometers by 12.4 kilometers.
the dimensions on the map are .5 centimeters by .62 centimeters.
the area in the real world is 10 * 12.4 = 124 square kilometers.
the area on the map is .5 * .62 = .31 centimeters.
the numbers check out so the logic looks good.
what remains to be determined is what the actual measurements are on the map versus the actual measurements in the real world.
i've assumed kilometers in the real world.
i guessed at centimeters on the map.
you can double check to see what they really are.
if they are different, then you'd need to change your analysis accordingly.
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