Final answer:
To find the area of ADEF, we use the ratio of corresponding side lengths between AABC and ADEF. The area of ADEF is 400 square centimeters.
Step-by-step explanation:
To find the area of ADEF, we need to determine the ratio between AABC and ADEF. Since AABC is similar to ADEF, their corresponding sides are proportional. Let's say the ratio between the side lengths of AABC and ADEF is 'x'.
Since the perimeter of AABC is five times the perimeter of ADEF, the ratio of their perimeters is also 'x'.
Now, the ratio of the areas of two similar figures is equal to the square of the ratio between their corresponding side lengths. So, the area of AABC is 100 square centimeters, which means (x^2) * area of ADEF = 100. Solving for x, we get x = 2. Therefore, the area of ADEF is (2^2) * 100 = 400 square centimeters.