A set of regular hexagons, each with a side length of 1 cm, is arranged in a tiling pattern inside a rectangular boundary. The hexagons are aligned such that some of them extend beyond the rectangle’s edges. Determine the exact area of the enclosing rectangle that fully contains the hexagonal tiling. Express the final answer in its simplest form.
By 
xtrapath
xtrapath
Hint :
It is solved by rotating the construction anticlockwise so that the bottom row of hexagons was sitting on the x-axis; the rectangle is then slanted, but it was easier to derive the equations for the lines which formed it from the vertices of the appropriate hexagons … thence their intersections, thence the area. It’s more co-ordinate geometry than trigonometry …