MathDB

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, that total area of the six triangular regions. Then

K=\tfrac{a}{b}

where

a

and

b

are relatively prime positive integers. Find

a + b

Problem Statement