From a piece of paper in the shape of a regular hexagon, sectors of circles with the centre at the vertices are removed as shown in the figure. Find the fraction of the vertices are removed as shown in the figure. Find the fraction of the piece of paper left. Also find the perimeter of the piece of paper left in terms of a side of the hexagon

Answer

`((3 sqrt3 - pi))/(3 sqrt3), (3 sqrt3 - pi ) (a^(2))/(2)` square units