Question

Can someone please help me with this?

Answer 1

`403.06 cm^2; 100.77cm^2`

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
`(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`