A sequence of convex polygons $\{P_n\}$, $n\geqslant0$, is defined inductively as follows. $P_0$ is an equilateral triangle with sides of length 1. Once $P_n$ has been determined, its sides are trisected; the vertices of $P_{n+1}$ are the interior trisection points of the sides of $P_n$. Thus, $P_{n+1}$ is obtained by cutting corners off $P_n$, and $P_n$ has $3\cdot2^n$ sides. ($P_1$ is a regular hexagon with sides of length $1/3$.) Express $\lim_{n\rightarrow\infty}Area(P_n)$ in the form $\sqrt{a}/b$, where a and b are positive integers. Please provide the value of a + b.

Let's think step by step and output the final answer within \boxed{}.
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