2022 MathCounts State Team Round #10

Consider the equilateral triangle ABC with sides of length 8 \sqrt{3} cm. A point in the interior of ABC is said to be “special” if it is a distance of 3 cm from one side of the triangle and a distance of 7 cm from another side. Consider the convex polygon whose vertices consist of the special points. What is the area of this polygon? Express your answer as a decimal to the nearest tenth.

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