Let's solve this step by step.

Part a) Finding the unknown side length

Looking at the diagram, we can break this compound shape into two rectangles:

1. Vertical side (total height): The total height consists of two parts:
   • The height on the left: $14 \, \text{cm}$
   • The height on the right: $3 \, \text{cm}$

The unknown height marked with a "?" is the remaining portion of the vertical side. We can find it by subtracting the given heights from the total height on the left side: $\text{Unknown side} = 14 \, \text{cm} - 3 \, \text{cm} = 11 \, \text{cm}.$

Thus, the unknown side length is 11 cm.

Part b) Finding the perimeter

The perimeter is the total distance around the shape. We can calculate it by adding the lengths of all the outer sides:

• Top side: 5 cm
• Right side: 11 cm (calculated in part a)
• Bottom-right side: 5 cm
• Bottom: 8 cm
• Left side: 14 cm
• Middle side: 3 cm

Now, sum all these side lengths to get the perimeter: $P = 5 \, \text{cm} + 11 \, \text{cm} + 5 \, \text{cm} + 8 \, \text{cm} + 14 \, \text{cm} + 3 \, \text{cm}$ $P = 46 \, \text{cm}.$

So, the perimeter of the shape is 46 cm.

Would you like further details or explanations? Here are some additional questions you can explore:

1. How would the perimeter change if the unknown side were longer or shorter?
2. Can this shape be broken down into any other simpler components?
3. How can you calculate the area of this compound shape?
4. What is the importance of understanding perimeter in real-life applications?
5. How does knowing one missing length help solve the problem of perimeter?

Tip: When working with compound shapes, it's helpful to break them into familiar geometric figures like rectangles and squares for easier calculations.