The problem involves finding the area of the given shape, which is a composite figure made up of rectangles. Let's break down the problem:

1. Identify the dimensions:

   • The entire width of the shape at the bottom is $9 \, \text{in}$.
   • The height of the two side rectangles is $6 \, \text{in}$.
   • The width of the two side rectangles is $3 \, \text{in}$ each.
   • The width of the middle rectangle (at the top of the "U" shape) is $4 \, \text{in}$, and its height is $4 \, \text{in}$.

2. Calculate the area of the entire rectangle if the middle part wasn't cut out:

   • Total width: $9 \, \text{in}$
   • Total height: $6 \, \text{in}$
   • Area of the large rectangle: $9 \, \text{in} \times 6 \, \text{in} = 54 \, \text{in}^2$

3. Subtract the area of the missing rectangle:

   • The area of the middle cut-out rectangle: $4 \, \text{in} \times 4 \, \text{in} = 16 \, \text{in}^2$

4. Calculate the area of the remaining shape:

   • Area of the shape = Area of the large rectangle - Area of the cut-out
   • $54 \, \text{in}^2 - 16 \, \text{in}^2 = 38 \, \text{in}^2$

Thus, the area of the given shape is 38 square inches.

Would you like any more details or have any questions about this solution?

Here are five related questions:

1. How would the area change if the width of the cut-out rectangle increased by 2 inches?
2. If the height of the entire shape was reduced by 1 inch, what would be the new area?
3. Can you think of another way to divide the shape into simpler shapes to find the area?
4. What is the perimeter of the original shape before the cut-out?
5. How would the problem change if the shape was rotated 90 degrees?

Tip: When dealing with composite figures, breaking them down into simpler shapes can make it easier to calculate areas.