Question 7
There is a regular hexagon-shaped kiosk in the middle of a garden. To get to the kiosk, there’s a spiral path that leads right up to one of the sides of the hexagon. To create the path, the builder used an interesting technique. He tied a rope counterclockwise around the kiosk and used a pencil attached to the end of the rope to draw the outer edge of the path starting from one vertex of the hexagon. After that, he untangled the rope clockwise to draw the inside border. The same process was repeated, starting from the next vertex of the hexagon, as shown in the diagram below. What is the total area (shaded area in the diagram not including the kiosk), in m², of the path to the kiosk if the kiosk measures 6 meters on each side? (Take $\pi=\frac{22}{7}$)
