Option C: Both 1 and 2
      Statement 1: It is possible to cut the sheet exactly into 4 square sheets.
         ○ The dimensions of the rectangular sheet are 20 cm by 8 cm.
         ○ To cut the sheet into square sheets, the side of each square must be a common divisor of both 20 cm and 8 cm.
         ○ The greatest common divisor (GCD) of 20 and 8 is 4.
         ○ Therefore, it is possible to cut the sheet into squares of side 4 cm.
         ○ The number of such squares that can be cut is:
           ○ Along the length: \( \frac{20}{4} = 5 \) squares
           ○ Along the breadth: \( \frac{8}{4} = 2 \) squares
         ○ Total number of squares = \( 5 \times 2 = 10 \).
         ○ However, the statement asks for exactly 4 square sheets, which can be achieved by cutting the sheet into squares of side 8 cm (2 squares along the length and 1 along the breadth), resulting in 2 squares, and then further cutting each into 2 smaller squares of side 4 cm.
         ○ Thus, it is possible to cut the sheet into exactly 4 square sheets of side 4 cm each.
     Statement 2: It is possible to cut the sheet into 10 triangular sheets of equal area.
         ○ The area of the rectangular sheet is \( 20 \times 8 = 160 \) square cm.
         ○ To cut the sheet into 10 triangular sheets of equal area, each triangle must have an area of \( \frac{160}{10} = 16 \) square cm.
         ○ A right-angled triangle with base and height such that \( \frac{1}{2} \times \text{base} \times \text{height} = 16 \) can be used.
         ○ For example, a triangle with base 8 cm and height 4 cm has an area of \( \frac{1}{2} \times 8 \times 4 = 16 \) square cm.
         ○ The sheet can be divided into such triangles by cutting along the diagonals of rectangles formed by dividing the sheet into smaller rectangles of dimensions 8 cm by 4 cm.
         ○ Therefore, it is possible to cut the sheet into 10 triangular sheets of equal area.
     Since both statements are correct, the correct answer is Option C: Both 1 and 2.