3. Five identical squares are placed to form a letter $$ L $$ as shown in the figure above. Walid decided to add another two squares that are identical to the five squares so the obtained figure has an axis of symmetry. In how many ways can this be done? A. 4 B. 5 C. 12 D. 8 E. 10

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To solve the problem, we need to analyze the current configuration of the five squares forming the letter $$ L $$ and determine how to add two more squares to create a figure with an axis of symmetry.

1. **Understanding the Current Configuration**: The current configuration of the $$ L $$ shape consists of five squares arranged in a way that resembles the letter $$ L $$. This shape has a vertical and a horizontal segment.

2. **Identifying Symmetry**: For the new configuration to have an axis of symmetry, we can consider two types of symmetry:
   - Vertical symmetry (a vertical line of symmetry)
   - Horizontal symmetry (a horizontal line of symmetry)

3. **Adding Two Squares**: We need to add two squares in such a way that the resulting figure maintains symmetry.

### Case 1: Vertical Symmetry
- If we add two squares to the left side of the $$ L $$, we can place them directly adjacent to the existing squares, mirroring the right side.
- Possible placements:
  1. Add two squares vertically on the left side.
  2. Add one square vertically on the left and one square horizontally at the bottom left.
  3. Add one square horizontally at the bottom left and one square horizontally at the bottom right.
  4. Add two squares horizontally at the bottom left.

### Case 2: Horizontal Symmetry
- If we add two squares to the top of the $$ L $$, we can place them directly adjacent to the existing squares, mirroring the bottom side.
- Possible placements:
  1. Add two squares horizontally on the top side.
  2. Add one square horizontally on the top and one square vertically at the top right.
  3. Add one square vertically at the top right and one square vertically at the bottom right.
  4. Add two squares vertically at the top right.

### Total Configurations
Now, we need to count the unique configurations that maintain symmetry:
- For vertical symmetry, we have 4 configurations.
- For horizontal symmetry, we also have 4 configurations.

However, we need to ensure that we are not double-counting any configurations that may fit both symmetry types.

After careful consideration, we find that the configurations are distinct and do not overlap.

### Conclusion
Thus, the total number of ways to add two squares to the existing $$ L $$ shape to create a figure with an axis of symmetry is $$ 4 + 4 = 8 $$.

The answer is $$ \boxed{8} $$.
There are 8 ways to add two squares to the $$ L $$ shape to create a figure with an axis of symmetry.

3. Five identical squares are placed to form a letter \( L \) as shown in the figure above. Walid decided to add another two squares that are identical to the five squares so the obtained figure has an axis of symmetry. In how many ways can this be done? A. 4 B. 5 C. 12 D. 8 E. 10

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