Find the area of the region inside the circle and outside the cardioid

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