A hexagonal park of side x cm is surrounded by a hexagonal fence..the distance between them is root 3... what is the area of bigger hexagon?

The length of the line joining the center of the hexagon to any of its vertices is the same as the length of the side of the hexagon.

Consider the bigger hexagon: The length of the line joining the center to one of its vertices is (length of the line joining the center to a vertex of the smaller hexagon + distance between the two hexagons) = (x + $$\sqrt3$$)

Area of the bigger hexagon = ($$\sqrt3/4$$)*$$side^2$$ = ($$\sqrt3/4$$)*$$(x + \sqrt3)^2$$