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AnswerOne instrument for measuring areas is a Planimeter.
Area is not normally measured directly: it is usually derived from measurements of lengths. Tools that may be used for that are micrometer, vernier callipers, ruler, measure tape, range-finder, odometer etc.
you can use a meter ruler or a measuring tape. but then, it depends on which measurements do you want to use. some people use centimeter, some use meter, some kilometer.
Well, if you want to know the name of an instrument wich is able to measure an area:
planimeter
http://en.wikipedia.org/wiki/Planimeter