Question 18
(MON 4) 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 $R_{A_i}^{\alpha}$ around $A_i$ by $\alpha$, $i=1,2,\ldots,n$.