2007 Cyprus MO/Lyceum/Problem 15

Problem

The reflex angles of the concave octagon $ABCDEFGH$ measure $240^\circ$ each. Diagonals $AE$ and $GC$ are perpendicular, bisect each other, and are both equal to $2$ .

The area of the octagon is

$\mathrm{(A) \ } \frac{6-2\sqrt{3}}{3}\qquad \mathrm{(B) \ } 8\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } \frac{6+2\sqrt{3}}{3}\qquad \mathrm{(E) \ } \mathrm{None\;of\;these}$

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2007 Cyprus MO, Lyceum (Problems)
Preceded by Problem 14	Followed by Problem 16
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2007 Cyprus MO/Lyceum/Problem 15

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