To solve this problem, we need to determine how many rectangles are necessary to create a grid containing $10$ squares, arranged in $5$ rows of $2$.

1. First, we need to understand the example provided. The example grid has $4$ squares arranged in a $2 \times 2$ configuration and uses $9$ rectangles.

2. In a $2 \times 2$ grid:

   • Each small square is enclosed by $4$ rectangles: $1$ for the top, $1$ for the bottom, $1$ for the left, and $1$ for the right.
   • These $4$ rectangles overlap with adjacent squares.
   • Total: $9$ rectangles for $4$ squares.

3. Now, consider the problem of arranging $10$ squares in $5$ rows of $2$:

   • This can be visualized as a $5 \times 2$ grid.

Let's calculate the number of rectangles needed for a $5 \times 2$ grid:

• Each internal horizontal and vertical line between squares will be counted.

$\text{Number of horizontal lines} = \text{rows} + 1 = 5 + 1 = 6$

$\text{Number of vertical lines} = \text{columns} + 1 = 2 + 1 = 3$

The total number of rectangles is the product of the number of horizontal and vertical lines:

$\text{Total rectangles} = \text{horizontal lines} \times \text{vertical lines} = 6 \times 3 = 18$

Thus, to create a grid containing $10$ squares arranged in $5$ rows of $2$, you need $18$ rectangles.

So, the correct answer is: $\boxed{18}$

Would you like details or have any questions?

Here are 8 related questions that expand on this information:

1. How many rectangles would be needed for a $3 \times 3$ grid?
2. What is the formula for calculating the number of rectangles in a $m \times n$ grid?
3. How many squares can be formed within a $4 \times 4$ grid?
4. If the arrangement was $4 \times 2$, how many rectangles would be required?
5. How does the number of rectangles change if the grid is expanded to $6 \times 2$?
6. How many unique squares can be found in a $5 \times 5$ grid?
7. What if the grid is $10 \times 1$? How many rectangles are needed then?
8. How would you calculate the number of rectangles for a $7 \times 3$ grid?

Tip: To easily determine the number of rectangles in a grid, consider the grid lines rather than the squares themselves.