 Kalyn cut rectangle R from a sheet of paper and then cut figure S from R. All the cuts were made
parallel to the sides of the original rectangle. In comparing R to S
(A) the area and perimeter both decrease
(B) the area decreases and the perimeter increases
(C) the area and perimeter both increase
(D) the area increases and the perimeter decreases
(E) the area decreases and the perimeter stays the same
1. Let's denote the dimensions of the original rectangle \( R \) as \( l \) (length) and \( w \) (width). The area of \( R \) is given by:
   \[
   \text{Area of } R = l \times w
   \]
   The perimeter of \( R \) is given by:
   \[
   \text{Perimeter of } R = 2l + 2w
   \]

2. Kalyn cuts figure \( S \) from \( R \), and all cuts are made parallel to the sides of the original rectangle. This means that \( S \) is a smaller rectangle or a shape that can be inscribed within \( R \).

3. Since \( S \) is cut from \( R \), the area of \( S \) must be less than the area of \( R \). Let the dimensions of \( S \) be \( l' \) and \( w' \), where \( l' \leq l \) and \( w' \leq w \). The area of \( S \) is:
   \[
   \text{Area of } S = l' \times w'
   \]
   Since \( l' \leq l \) and \( w' \leq w \), it follows that:
   \[
   l' \times w' \leq l \times w
   \]
   Therefore, the area of \( S \) is less than or equal to the area of \( R \).

4. Now, consider the perimeter of \( S \). The perimeter of \( S \) is given by:
   \[
   \text{Perimeter of } S = 2l' + 2w'
   \]
   Since \( l' \leq l \) and \( w' \leq w \), it follows that:
   \[
   2l' + 2w' \leq 2l + 2w
   \]
   Therefore, the perimeter of \( S \) is less than or equal to the perimeter of \( R \).

5. Since both the area and the perimeter of \( S \) are less than or equal to those of \( R \), and given that \( S \) is a proper subset of \( R \) (i.e., \( S \) is strictly smaller than \( R \)), both the area and the perimeter of \( S \) must be strictly less than those of \( R \).

Conclusion:
\[
\boxed{A}
\]