Mathematical and Physical Journal
for High Schools
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Problem C. 850. (April 2006)

C. 850. An arbitrary interior point of a regular hexagon of unit side is reflected about the midpoint of each side, respectively. Calculate the area of the resulting hexagon.

(5 pont)

Deadline expired on May 18, 2006.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás: A felezőpontok szabályos hatszöget alkotnak, ennek kétszeres nagyítása a kérdéses hatszög. Vagyis az is szabályos. Az oldalának hossza: 2\cdot F_1F_2=\sqrt3. Vagyis

T=6t=6\cdot{\left(\sqrt3\right)^2\cdot\sqrt3\over4}={9\sqrt3\over2}.


Statistics:

215 students sent a solution.
5 points:132 students.
4 points:33 students.
3 points:15 students.
2 points:23 students.
1 point:7 students.
0 point:5 students.

Problems in Mathematics of KöMaL, April 2006