To find the area of the sidewalk with height \( h \) and width \( w \), you can use the formula for the area of a rectangle, which is given by:
\[ \text{Area} = \text{height} \times \text{width} \]
Given that:
- \( h = x \)
- \( w = x + 1 \)
Substituting these values into the area formula:
\[ \text{Area} = h \times w = x \times (x + 1) \]
Now, simplify the expression:
\[ \text{Area} = x(x + 1) = x^2 + x \]
Therefore, the expression that describes the area of the sidewalk is:
\[ \text{Area} = x^2 + x \]