Let $ F_n$ be a set of all possible connected figures, that consist of $ n$ unit cells. For each element $ f_n$ of this set, let $ S(f_n)$ be the area of that minimal rectangle that covers $ f_n$ and each side of the rectangle is parallel to the corresponding side of the cell. Find $ max(S(f_n))$,where $ f_n\in F_n$?

Remark: Two cells are called connected if they have a common edge.
1. **Understanding the Problem:**
   We need to find the maximum area \( S(f_n) \) of the minimal rectangle that covers any connected figure \( f_n \) consisting of \( n \) unit cells. The sides of the rectangle must be parallel to the sides of the unit cells.

2. **Initial Observation:**
   The minimal rectangle that covers \( f_n \) will have its sides parallel to the sides of the unit cells. The area of this rectangle is determined by the maximum horizontal and vertical extents of the figure.

3. **Perimeter Consideration:**
   The perimeter \( P \) of the minimal covering rectangle is related to the number of unit cells \( n \). For a connected figure, the perimeter \( P \) is bounded by \( P \leq 2n + 2 \).

4. **Proof of Perimeter Bound:**
   - Consider a figure that is "almost connected," meaning each pair of cells has a vertex in common. The maximum perimeter of the minimal covering rectangle for such a figure is \( 4n \).
   - To make the figure connected, we need to shift the cells such that they share edges. Each shift reduces the perimeter by at least 2.
   - We need \( n-1 \) shifts to make the figure fully connected. Each shift reduces the perimeter by at least 2, so the total reduction is at least \( 2(n-1) \).
   - Therefore, the perimeter of the connected figure is at most:
     \[
     4n - 2(n-1) = 4n - 2n + 2 = 2n + 2
     \]

5. **Maximizing the Area:**
   - The area \( S(f_n) \) of the minimal rectangle is given by the product of its width and height.
   - To maximize \( S(f_n) \), we need to consider the configuration of the cells. The most stretched configuration would be a straight line of \( n \) cells, either horizontally or vertically.
   - For a straight line of \( n \) cells, the minimal covering rectangle has dimensions \( 1 \times n \) or \( n \times 1 \), giving an area of \( n \).

6. **Conclusion:**
   - The maximum area \( S(f_n) \) of the minimal rectangle that covers any connected figure \( f_n \) consisting of \( n \) unit cells is \( n \).

The final answer is \( \boxed{n} \)