To find the perimeter of this shape, we need to add up the lengths of all its sides. The shape has a combination of rectangular sections with known lengths and two unknown side lengths, $u$ and $v$, which we need to determine using the information provided.

Here's the approach:

1. Identify the given side lengths:

   • One vertical side is 11.8 km.
   • One horizontal side is 8 km.
   • Another vertical side is 3.5 km.
   • Another horizontal side is 3 km.

2. Determine the unknown side lengths $u$ and $v$:

   • Since the vertical side from the top to the bottom is divided into parts 11.8 km (left side) and 3.5 km (right side), we can find $u$ by subtracting 3.5 km from 11.8 km. $u = 11.8 \text{ km} - 3.5 \text{ km} = 8.3 \text{ km}$
   • For $v$, we consider the total horizontal span of 8 km, which is divided into 3 km (top part) and $v$ (bottom part). $v = 8 \text{ km} - 3 \text{ km} = 5 \text{ km}$

3. Calculate the perimeter:

   • Now that we have all the side lengths, we can add them up: $\text{Perimeter} = 11.8 + 3 + 3.5 + 8 + u + v$ Substituting $u = 8.3$ km and $v = 5$ km: $\text{Perimeter} = 11.8 + 3 + 3.5 + 8 + 8.3 + 5 = 39.6 \text{ km}$

So, the perimeter of the shape is 39.6 km.

Would you like further details on any step?

Here are some related questions for further exploration:

1. How would the perimeter change if one side length was increased or decreased?
2. How can we determine the area of this shape?
3. What if one of the side lengths was unknown; how could we solve for it?
4. Can we use this method for any irregular shape?
5. How would the perimeter change if it was scaled up by a factor of 2?

Tip: When solving for unknowns in composite shapes, breaking down each part systematically can simplify the solution process.