Took me a while to solve but here it is:
1) The side of the square is worth 4, as seen up in the picture.
2) The picture shows only parts of two circles which intersect each other. The equation of the circle is x² + y² = r², where r is the radius. The radius of the smaller circle is 4, and the bigger is 8. Here is the visual representation:
http://goo.gl/UjYOqD
3) To be able to calculate the area, we need to transform the equations into functions:
http://goo.gl/cbyXIO
4) Now we calculate the area between the two functions. This can be done by integrating the difference in the interval:
http://goo.gl/hwhtRX
Therefore, the area of that thing is 1.727 square units.
I couldnt find a way of calculating it without the computer : ( but here is the answer for those who were curious.
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