Question 4
In equiangular octagon $CAROLINE,$ $CA = RO = LI = NE = \sqrt{2}$ and $AR = OL = IN = EC = 1.$ 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 $a + b.$