In equiangular octagon CAROLINE, C A=R O=L I=N E=\sqrt{2} and A R=O L=I N=E C=1. The self-intersecting octagon CORNELIA encloses six non-overlapping triangular regions. Let K be the area enclosed by CORNELIA, that is, the total area of the six triangular regions. Then K=\frac{a}{b}, where a and b are relatively prime positive integers. Find a+b.