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Let $Q$ be a unit square in the plane with corners at $(0,0),(0,1),(1,0)$ and $(1,1)$. Let $B$ be a ball of radius $1$ in the plane centered at the origin $(0,0)$. Let $Q+B$ denote the set of all vectors in the plane of the form $v+w,$ where $v \in Q$ and $w \in B$. The area of $Q+B$ is:

  1. $5+\pi$
  2. $4+\pi$
  3. $3+\pi$
  4. $2+\pi$
  5. $1+\pi$

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