2021 WSMO Team Round Problems/Problem 13

Problem

Square $BCDE$ is drawn outside of equilateral triangle $ABC.$ Regular hexagon $DEFGHI$ is drawn outside of square $BCDE.$ If the area of triangle $AED$ is 3, then the area of triangle $AGH$ can be expressed as $a\sqrt{b}-c,$ where $b$ is not divisible by the square of any prime. Find $a+b+c.$

Proposed by pinkpig

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2021 WSMO Team Round Problems/Problem 13

Problem

Solution