
Arturo O. answered 02/11/17
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There is another way that sounds a bit unorthodox, but was actually used in the real world:
Carefully draw the shape of unknown area A on paper. Cut out the shape and weigh it on a delicate scale. Suppose the weight of the cut out shape is w. Draw a shape of known area A1 to the same scale as area A on the same paper. Cut it out and weigh it. Suppose it weighs w1. Then
A/A1 = w/w1 ⇒
w = (A/A1)w1
This was actually used in labs a few decades ago when data was plotted by hand. Today we have instruments that draw curves and calculate areas under the curves by numerical integration in real time, so this method is not used much anymore. But if you do not have the instruments, this gives you a "poor person's" way of getting the area.