On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilateral triangle, another equilateral triangle of side length 1 is constructed. The interiors of the square and the 12 triangles have no points in common. Let R be the region formed by the union of the square and all the triangles, and S be the smallest convex polygon that contains R. What is the area of the region that is inside S but outside R?
<spanclass=′latex−bold′>(A)</span>41<spanclass=′latex−bold′>(B)</span>42<spanclass=′latex−bold′>(C)</span>1<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>23