1. **Problem Statement:** We have a large square with side length 1 dissected into 14 smaller squares. We need to find the area of the shaded smaller square. 2. **Key Idea:** The total area of the large square is 1 (since side length is 1). The sum of the areas of all 14 smaller squares must equal 1. 3. **Approach:** Since the problem is a classic dissection puzzle, the side lengths of the smaller squares are related such that their areas sum to 1. The shaded square is one of these smaller squares. 4. **Given Options:** The possible areas for the shaded square are: - (A) $\frac{1}{49}$ - (B) $\frac{1}{36}$ - (C) $\frac{1}{25}$ - (D) $\frac{1}{18}$ - (E) $\frac{1}{12}$ 5. **Reasoning:** Among these, $\frac{1}{49}$ corresponds to a square with side length $\frac{1}{7}$, $\frac{1}{36}$ corresponds to side length $\frac{1}{6}$, $\frac{1}{25}$ corresponds to side length $\frac{1}{5}$, and so on. 6. **Conclusion:** The shaded square's side length is $\frac{1}{7}$, so its area is $\frac{1}{49}$. **Final answer:** $\boxed{\frac{1}{49}}$ (Option A)