B5. A regular hexagon is divided into seven pieces by lines parallel to the sides as shown in the figure. Four of the pieces are equilateral triangles, the lengths of whose sides are indicated in the figure. What is the length of the sides of the regular hexagon?

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## C-Problems

For the C-Problems, not only the answer is important; your reasoning and the method of solving must also be clearly written. Solve each C-Problem on a separate sheet of paper. Each correctly worked-out C-Problem is worth 10 points. Partial solutions can also earn points. Therefore, write everything clearly and submit your scratch paper (per problem!) as well.
B5. 19 By dividing the regular hexagon into six small equilateral triangles, we see that the length of the long diagonal $A C$ is twice the side length of the hexagon. We calculate three times the side length, namely $|A B|+|B C|+|C D|$. Line segment $A B$ is a side of a parallelogram, of which the side parallel to it has length $11+16=27$. Therefore, $|A B|=27$.

Since triangle $B C E$ is equilateral, it follows that $|B C|=|E B|$.

Since $B C D F$ is a parallelogram, it follows that $|C D|=|B F|$.

Finally, we read off that $|E B|+|B F|=|E F|=5+16+9=30$.

All together, we find that three times the side length is equal to

$$
|A B|+|B C|+|C D|=27+|E B|+|B F|=27+30=57 \text {. }
$$

The side length is thus $\frac{57}{3}=19$.
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## C-problems