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BaileyBelmont
ok. 
if I got this right, you need the area inside the cardioid but without actual circle in it. Well, if so, it is easy:

area(cardioid)=6*Pi*r^2 
area(circle)=Pi*r^2
area(cardioid-circle)=5*Pi*r^2
where r=radius of the circle. and r^2=r*r


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