https://file.aiquickdraw.com/mathbot/file/1727403572894kz3kw31l.jpg

This problem is asking you to determine if the provided statements are sufficient to calculate the area of the rectangle depicted.

### Step-by-step breakdown:

1. **Diagram Layout**:
   - The figure shows a rectangle divided into two smaller rectangles:
     - One with dimensions \( 6 \times z \).
     - The other with dimensions \( x \times y \).
   
2. **Objective**:
   - We need to determine the area of the entire figure (which is the sum of the areas of the two rectangles).

   The total area of the figure is given by:
   \[
   \text{Total Area} = (6 \times z) + (x \times y)
   \]

3. **Given Statements**:
   - **Statement (1):** \( x = 14 \)
   - **Statement (2):** \( y = 35 \)

4. **Analysis**:
   - To find the total area, we need both \( z \) and \( y \). Knowing \( x = 14 \) helps with one part, but it doesn’t directly tell us \( z \), the width of the first rectangle. Likewise, knowing \( y = 35 \) only gives us the height of the second rectangle but doesn’t directly help us with \( z \) either.
   
   Let's assess each option:

   **Option A**:
   - Statement (1) alone is not sufficient, as we still don't know \( z \), which is necessary to calculate the area of the first rectangle.
   - So, **A is false**.

   **Option B**:
   - Statement (2) alone is also insufficient because while it gives us \( y \), we still need \( z \) to calculate the total area.
   - So, **B is false**.

   **Option C**:
   - Both statements together give \( x = 14 \) and \( y = 35 \), but we still don’t know the value of \( z \) to compute the area of the first rectangle.
   - Thus, **C is false**.

   **Option D**:
   - This suggests that either statement is sufficient alone, but we’ve already determined both statements alone are insufficient.
   - **D is false**.

   **Option E**:
   - Neither statement is sufficient on its own or together, because we still lack information about \( z \).
   - Therefore, **E is the correct answer**.

### Conclusion:
The correct answer is **E**. Neither statement alone nor together provides enough information to answer the question about the total area.

Let me know if you want further clarification or have additional questions!

### Related questions:
1. How do you calculate the area of a composite figure?
2. What role does knowing both dimensions (length and width) play in calculating area?
3. Can we infer the missing value \( z \) with any additional information?
4. How would the problem change if a total area were provided instead?
5. Is there a specific property of rectangles that we use when dividing them?

### Tip:
Always ensure you have enough independent variables to solve for an area or any geometric problem!

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Learn how to calculate the area of composite rectangles given specific dimensions. This problem involves understanding how to work with rectangular areas and involves algebraic concepts. Suitable for students in Grades 8-10.

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