Question

Can someone please help me with this?

Answer 1

Answer:

$403.06 cm^2; 100.77cm^2$

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 $(n-2)\pi = 10\pi$. That makes each angle measure $\frac{10}{12}\pi$.

That allows us to split the whole figure in 12 isosceles triangles with (congruent) angles of $\frac5{12}\pi$. Consider just one, red in my picture. The height of that triangle - orange "vertical" line -  can be found with some trigonometry as $3tan \frac5{12}\pi \approx 11.2 cm$

At this point one triangle has area $\frac12 \cdot 6\cdot 11.2 = 33.6 cm^2$ and the whole cookie has area as 12 triangles $403.06 cm^2$.

After her eating spree, you're left with 3 triangles, for a grand total of $100.77 cm^2$