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Math Help - Maps

  1. #1
    Member helloying's Avatar
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    Maps

    The scale of a map is 1:300 000

    Find the actual area of the village, in km^2, if the area on the map is 3cm^2
    Last edited by helloying; October 31st 2008 at 08:25 PM.
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  2. #2
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    Quote Originally Posted by helloying View Post
    The scale of a map is 1:300 000

    Find the actual area of the village, in km^2, if the area on the map is 3cm^2
    It tells us that 1cm on the map gives 300,000 cm in real life.

    If we had a square of side length 1cm, it would correspond to a square of side lengths 300,000cm. So a square with area 1cm \times 1cm = 1cm^2 would correspond to a square of area 300,000cm \times 300,000cm = 90,000,000,000cm^2.

    So if the area on the map is 3cm^2 then it would correspond to an area of 3 \times 90,000,000,000cm^2 = 270,000,000,000cm^2.

    Since there are 100cm in 1 metre, there are 100^2cm^2=10,000cm^2 in 1m^2.

    So that means that 270,000,000,000cm^2 = 27,000,000m^2.

    Since there are 1000m in 1km, there are 1000^2m^2 = 1,000,000m^2 in 1km^2.

    So 27,000,000m^2 = 27km^2.


    Therefore the actual area that is represented by this map is 27km^2.
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  3. #3
    Member helloying's Avatar
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    OH I SEE! thank you very much. I have been very stupid. i understand now
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