Total Area of a Convex Hexagon

Consider a convex hexagon $ABCDEF$ where:

- The lengths of the sides are $AB = 8$, $BC = 6$, $CD = 12$, $DE = 10$, $EF = 5$, and $FA = 7$.

- The hexagon can be divided into four triangles by drawing diagonals $AC$, $BD$, and $CE$.

What is the total area of the hexagon if the angles at vertices $A$, $B$, $C$, $D$, $E$, and $F$ are all $120^ ext{o}$?