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 $9$ 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.
