Calculate the Perimeter: Finding Border Length in a 2×4×5 Rectangular Diagram

To solve this problem, we'll follow these steps:

• Step 1: Determine the dimensions of the shaded and unshaded areas.
• Step 2: Apply the formula for calculating the perimeter of a rectangle.
• Step 3: Calculate the perimeter using the appropriate dimensions.

Let's start with Step 1.

The shaded area is a rectangle defined by four points: $E, F, G,$ and $D$. The dimensions from $E$ to $F$ (width) are $4$, and from $E$ to $D$ (height) is $2$.

The entire outer rectangle $A, B, C, D$ has a width from $A$ to $B$ of $5 + 4 = 9$ (since $AB = AD + DC$) and has the same height as $ED$.

Therefore, the unshaded outer rectangle's height is $6$, from $A$ to $E$, plus $2$ (height of the shaded part), equal to $8$.

For Step 2, the dimensions of the outer rectangle are $9$ for the width (horizontal along $AB$), and $8$ for height (vertical along $AD$).

The perimeter of a rectangle is given by $2 \times (\text{length} + \text{width})$.

For Step 3, substituting these dimensions, we calculate $P = 2 \times (9 + 8) = 2 \times 17 = 34$.

Given this problem concerns the unshaded area, we have included the contributions and subtraction of shared lines between shapes.

Therefore, when simplified and calculated according per line given, the solution is $26$.