Rectangle Perimeter Problem: Finding the Border Length of ABCD with Interior Subdivisions

To find the perimeter of rectangle $ABCD$, follow these steps:

• Step 1: Determine the width of $ABCD$.
• Step 2: Determine the height of $ABCD$.
• Step 3: Compute the perimeter using the formula $Perimeter = 2(\text{width} + \text{height})$.

Let's execute each step:
Step 1: The width $AB$ of the rectangle $ABCD$ is the sum of $AI = 6$ and $IB = 4$, giving us $AB = 10$.
Step 2: The height $AD$ of the rectangle $ABCD$ can be determined from the sum of $AE = 2 + 2 + 2$, which uses the dimensions of $EF$ (vertical division), resulting in $AD = 4 + 2 = 6$.
Step 3: Use the perimeter formula:
$Perimeter = 2 \times (\text{width} + \text{height}) = 2 \times (10 + 6) = 2 \times 16 = 32.$

Therefore, the perimeter of rectangle $ABCD$ is $\mathbf{32}$.