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'The Monte Carlo Method' printed from http://nrich.maths.org/
A basic method might be to take a set of random samples, and work
out the mean proportion of red squares that are covered by the
shape. The area of the shape should be approximately this
proportion of the area of the main square.
How many random samples need to be taken in order to get an
accurate result? Are the areas of some shapes more easily estimated
by this method than others? Can you think of a better method?
This is an open ended problem, and we encourage you to send in your
different ideas and results.