(;) Semicolon Math: Star in a hexagon

Let \(ABCDEF\) be a regular hexagon with side length \(1.\) Let \(G\) be the intersection of \(AC\) and \(BF,\) \(H\) be the intersection of \(AC\) and \(BE,\) \(I\) be the intersection of \(CF\) and \(BE,\) \(J\) be the intersection of \(CF\) and \(AE,\) and \(K\) be the intersection of \(AE\) and \(BF.\) The area of \(AGBHCIEJFK\) can be expressed in form \(\frac{a\sqrt{b}}{c}\) where \(a\) and \(c\) are relatively prime and \(b\) is not divisible by the square of any prime. Find \(a+b+c.\)