The dimensions for the rectangles are unknown 

Thanks for the clarification! If the dimensions of the rectangles are unknown, let's solve the problem symbolically, using variables for the unknown dimensions.

### Given:
1. Each rectangle is identical, with an unknown length \( l \) and height \( h \).
2. The height of \( AB \) is 4 times the height of \( AE \).
3. The shape \( ABCDE \) is made up of 5 rectangles.

### Problem Breakdown:

1. **Length of \( AE \):**
   - \( AE \) represents the length of one rectangle, so:
   \[
   AE = l
   \]

2. **Length of \( AB \):**
   - According to the problem, the height of \( AB \) is 4 times the height of \( AE \). Since the height of \( AE \) corresponds to the height of one rectangle:
   \[
   AB = 4 \times h
   \]

3. **Area of the shape \( ABCDE \):**
   - The shape is made up of 5 rectangles, so the total area is the sum of the areas of all 5 rectangles.
   - The area of one rectangle is \( l \times h \).
   - The total area of the shape is:
   \[
   \text{Area of ABCDE} = 5 \times (l \times h) = 5lh
   \]

### Final Answers:
- Length of \( AE = l \) (in terms of the unknown length \( l \))
- Length of \( AB = 4h \) (in terms of the unknown height \( h \))
- Area of \( ABCDE = 5lh \) (in terms of the unknown length \( l \) and height \( h \))

Would you like further details or help with a specific part of the problem?

### Follow-up Questions:
1. If the total area is given, can you find \( l \) and \( h \)?
2. How would the problem change if the ratio of the heights \( AB \) and \( AE \) was different (e.g., 3 times instead of 4)?
3. Can you express the perimeter of the shape \( ABCDE \) in terms of \( l \) and \( h \)?
4. How would you approach solving for \( l \) and \( h \) if you were given additional dimensions?
5. What happens to the area if both \( l \) and \( h \) are doubled?

### Tip:
Using variables to represent unknown quantities is a powerful way to generalize a problem and make it easier to find relationships between different parts of the shape.

Explore how to solve a geometry problem involving rectangles with unknown dimensions. Learn how to use variables to represent lengths and heights, and calculate the area of a complex shape made up of identical rectangles. Suitable for high school students.

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