Answer: D. $\text{329}$

Explanation:1. Understand the problem: We need to find the area of a rectangle. The width is given, and the length is described in relation to the width.

2. Determine the dimensions of the rectangle: The width ($w$) of the rectangle is $\text{7}$ centimeters. The length ($l$) of the rectangle is $\text{40}$ centimeters longer than the width. So, $l = w + \text{40}$ centimeters. $l = \text{7} + \text{40} = \text{47}$ centimeters.

3. Calculate the area of the rectangle: The area ($A$) of a rectangle is given by the formula $A = \text{length} \times \text{width}$. $A = l \times w$ $A = \text{47} \times \text{7}$.

To calculate $\text{47} \times \text{7}$: $A = (\text{40} + \text{7}) \times \text{7}$ $A = (\text{40} \times \text{7}) + (\text{7} \times \text{7})$ $A = \text{280} + \text{49}$ $A = \text{329}$. The area is $\text{329}$ square centimeters.

4. Compare with the given options: [A] $\text{7}$ [B] $\text{14}$ [C] $\text{54}$ [D] $\text{329}$ The calculated area $\text{329}$ square centimeters matches option [D].

5. Conclusion: The area of the rectangle is $\text{329}$ square centimeters.