Geometry 1

You are given a convex polygon with $N$ sides. You have to answer $Q$ queries. The $i^{th}$ query is described by two integers $v_i, t_i$. In this query, all sides of the polygon start moving parallel to their respective perpendicular vector away from the centroid with a constant velocity of $v_i \frac{units}{sec}$. Output the final area covered by $N$ sides of the polygon after time $t_i$ seconds