Hexagonal Areas

Add the following lines to make $6$ congruent triangles:

There are $4$ blue triangles and $2$ yellow triangles, so the ratio of areas is $\frac{4}{2} = \boxed{2}$ .

The yellow region is shared $\cfrac{1}{6}$ of the total area while the blue region is shared $\cfrac{2}{6}$ of total area.

Therefore, the ratio is $\boxed{2}$ .

We note that $\angle DCE = \angle ECF = 30^{\circ}$ , and that $\overline{CF} = 2 \overline{CD}$ .

We have that

$[CDE] = \frac{1}{2} \overline{CD} \hspace{4pt} \overline{CE} \sin 30^{\circ}$ , and

$[CEF] = \frac{1}{2} \overline{CE} \hspace{4pt} \overline{CF} \sin 30^{\circ}$

Dividing the second by the first, gives a ratio of $\boxed{2}$ .