https://file.aiquickdraw.com/mathbot/file/1727379787426gk5aj046.jpg

To solve the problem, we need to find the area of Rectangle \( E \).

### Given Information:
1. **Rectangle \( A \)**: 
   - Dimensions: \( 2 \text{ cm} \times 4 \text{ cm} \)
   - Area: \( 2 \times 4 = 8 \text{ cm}^2 \)
   
2. **Rectangles \( B, C, D, \) and \( E \)** are scaled copies of Rectangle \( A \).

3. From the image, the rectangles \( B, C, D, \) and \( E \) are arranged within a larger rectangle, and their layout indicates that the large rectangle has a height of \( 8 \text{ cm} \) (same as Rectangle \( A \)) and the sum of the widths of \( C \) and \( E \) gives the width of the larger rectangle.

### Calculation Steps:
1. **Determine dimensions of Rectangle \( E \)**:
   - Width of \( C \): same as \( A \) because they are scaled copies. Thus, \( C \)'s width is \( 2 \text{ cm} \).
   - Width of \( E \): remaining width of the large rectangle, which is \( 4 \text{ cm} \) (total width) - \( 2 \text{ cm} \) (width of \( C \)) = \( 2 \text{ cm} \).
   - Height of \( E \): Since \( E \) is below \( A \), and height of \( A \) is \( 4 \text{ cm} \), \( E \)'s height would be \( 8 \text{ cm} - 4 \text{ cm} = 4 \text{ cm} \).

2. **Calculate the area of Rectangle \( E \)**:
   - Area = \( 2 \text{ cm} \times 4 \text{ cm} = 8 \text{ cm}^2 \).

Hence, the area of Rectangle \( E \) is **8 cm²**.

Would you like any more details or have any other questions?

### Related Questions:
1. What is the area of Rectangle \( B \)?
2. What is the perimeter of the larger rectangle formed by \( B, C, D, \) and \( E \)?
3. If the scale factor between \( A \) and \( D \) is known, can we determine its dimensions?
4. What would be the effect on the area if the width of Rectangle \( E \) was doubled?
5. How many rectangles equivalent to \( A \) can fit in the space occupied by \( E \)?

**Tip:** When dealing with similar shapes, the ratio of areas is equal to the square of the ratio of their corresponding lengths.

Learn how to find the area of Rectangle E in a geometry problem involving scaled copies of rectangles. This step-by-step solution covers key concepts such as area of rectangles, scaling, and geometry principles. Suitable for students in Grades 6-8.

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