Answer:
[tex]403.06 cm^2; 100.77cm^2[/tex]
Step-by-step explanation:
Ok, step 1. What's the measure of the internal angle of a dodecagon? After some splitting in triangles you get that's [tex](n-2)\pi = 10\pi[/tex]. That makes each angle measure [tex]\frac{10}{12}\pi[/tex].
That allows us to split the whole figure in 12 isosceles triangles with (congruent) angles of [tex]\frac5{12}\pi[/tex]. Consider just one, red in my picture. The height of that triangle - orange "vertical" line - can be found with some trigonometry as [tex]3tan \frac5{12}\pi \approx 11.2 cm[/tex]
At this point one triangle has area [tex]\frac12 \cdot 6\cdot 11.2 = 33.6 cm^2[/tex] and the whole cookie has area as 12 triangles [tex]403.06 cm^2[/tex].
After her eating spree, you're left with 3 triangles, for a grand total of [tex]100.77 cm^2[/tex]
