To find the ratio of the area of ABFE to the area of EFCD, we need to calculate the areas of both these figures separately. Let's break down the solution step by step:

1. Identify the given information:
- AB is parallel to DC.
- AB = 2 cm and DC = 3 cm.
- E and F are the midpoints of the nonparallel sides.

2. Draw the trapezium ABCD and mark the midpoints E and F:
- Draw a horizontal line to represent AB.
- Draw a longer line below the horizontal line to represent DC.
- Join the endpoints of both lines with diagonal lines to form a trapezium ABCD.
- Mark the midpoints E and F on the nonparallel sides of the trapezium.

3. Divide the trapezium into two triangles:
- Draw a line joining EF, dividing the trapezium into two triangles, AEF and CDF.

4. Calculate the area of each triangle:
- Since E and F are midpoints, we can say that EF is parallel to AB and DC.
- Therefore, the triangles AEF and CDF are similar.
- The ratio of the lengths of corresponding sides is the same as the ratio of the areas of similar triangles.
- AE:CD = AF:CB = EF:DC = 1:2
- Therefore, the area of triangle AEF is (1/2) * (1/2) = 1/4 times the area of triangle ACD.
- Similarly, the area of triangle CDF is also 1/4 times the area of triangle ACD.

5. Calculate the area of trapezium ABFE:
- The area of trapezium ABFE is equal to the sum of the areas of triangles AEF and CDF.
- Therefore, the area of trapezium ABFE = (1/4 + 1/4) times the area of triangle ACD.
- Simplifying, the area of trapezium ABFE = 1/2 times the area of triangle ACD.

6. Calculate the area of trapezium EFCD:
- Since the area of trapezium ABFE is 1/2 times the area of triangle ACD, the area of trapezium EFCD is also 1/2 times the area of triangle ACD.

7. Find the ratio of the areas:
- The ratio of the area of ABFE to the area of EFCD is equal to (1/2)/(1/2) = 1/1 = 1:1.

8. Simplify the ratio:
- Since the ratio 1:1 can be simplified further, we can say that the ratio of the area of ABFE to the area of EFCD is 1:1 = 9:9.

Therefore, the correct answer is option C, 9:11.