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The area of the 4 quartercircles inside the square is about 113 cm^{2} and the area of the square is 100 cm^{2} so about 13cm^{2} wouldn't fit in the square. This is the same as your area of overlap. How much the quarter circles overlap depends on the radius of the circles. If you want to try it out for yourself try cutting a 10cm by 10cm square out of paper and circles of various sizes. If you quarter the circles and rearrange them you will see this is true. Hope this helps, Anthony wrote back
Anthony, I want to find 1/4 the area of the region enclosed by the 4 circles or radius 10, the region you labeled R. The way to determine that area is to note that it is 1/12 the area of the circle (from 30^{o} to 60^{o}) minus the area of two triangles whose base is 5(sqrt(3))  5 and height is 5. Chris  


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