Always a romantic, Marris decided to bake his girlfriend a cookie in the shape of a regular dodecagon ($12$-gon) for Valentine’s Day.  

1. If the edge of the dodecagon is $6$ cm, what is the area of the top of the cookie?

   Hint (a):

   Try splitting the cookie into triangles.
   What information do you already know about these triangles' angles and sides?
   Can you use this to find the area of a single triangle?

   More Help (a):

   

   
   

2. His girlfriend decides to divide the cookie into $12$ congruent pieces. After $9$ of the pieces have been eaten, what area of the cookie is left?

   Hint (b):

   Multiply the area of a single triangle by the number of triangles remaining after some have been eaten.