Given a convex polygon
with area
and a point
in the same plane, determine the area of polygon
where
is the image of
under rotation
around
by
%V0
Given a convex polygon $A_1A_2 \ldots A_n$ with area $S$ and a point $M$ in the same plane, determine the area of polygon $M_1M_2 \ldots M_n,$ where $M_i$ is the image of $M$ under rotation $R^{\alpha}_{A_i}$ around $A_i$ by $\alpha_i, i = 1, 2, \ldots, n.$
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