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If the radius of the circle is R, and the length of the flat region is c, then the area of the circle containing a flat is:

A = R2 [Pi - Arcsin(c / 2R)] + [(c / 2) (R2 - (c / 2)2)1/2]

After some calculus and algebra

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Q: How can you find the area of a circle with one flat side?
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