In the figure, point $P, Q,R,S$ lies on the side of the rectangle $ABCD$. 
[img]https://1.bp.blogspot.com/-Ff9rMibTuHA/X9PRPbGVy-I/AAAAAAAAMzA/2ytG0aqe-k0fPL3hbSp_zHrMYAfU-1Y_ACLcBGAsYHQ/s426/2020%2BIndonedia%2BMO%2BProvince%2BP2%2Bq1.png[/img]
If it is known that the area of the small square is $1$ unit, determine the area of the rectangle $ABCD$.
1. **Identify the side lengths of the small square:**
   - Given that the area of the small square is \(1\) unit, the side length of the small square is \(\sqrt{1} = 1\) unit.

2. **Determine the coordinates of points \(P, Q, R, S\):**
   - Assume the coordinates of \(C\) are \((0,0)\).
   - Since \(CS\) is along the vertical side of the rectangle and \(S\) is at the top of the small square, \(CS = 2\) units.
   - \(R\) is diagonally opposite to \(C\) in the small square, so \(CR = \sqrt{1^2 + 2^2} = \sqrt{5}\) units.

3. **Analyze the parallelogram \(CRQS\):**
   - Since \(CRQS\) is a parallelogram, the opposite sides are equal. Therefore, \(QS = CR = \sqrt{5}\) units.

4. **Determine the dimensions of the rectangle \(ABCD\):**
   - Let the length of the rectangle be \(l\) and the width be \(w\).
   - From the given information, \(CS = w = 2\) units.
   - Since \(R\) is on the side \(CD\) and \(CR = \sqrt{5}\), we can infer that the length \(l\) must be such that the diagonal \(CR\) fits within the rectangle.

5. **Calculate the area of the rectangle:**
   - The area of the rectangle \(ABCD\) is given by \(l \times w\).
   - Given \(w = 2\) units and \(l = \sqrt{5}\) units, the area is:
     \[
     \text{Area} = l \times w = \sqrt{5} \times 2 = 2\sqrt{5} \text{ square units}
     \]

The final answer is \(\boxed{2\sqrt{5}}\) square units.