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The problem provided involves finding the exact perimeter of composite shapes. Let's analyze and solve the two composite shapes in the image.

### (a) First Composite Shape:
This shape is a rectangle combined with a semicircle.

- **Rectangle:** The rectangle has a length of 6 cm and a height of 4 cm.
- **Semicircle:** The semicircle is attached to the top of the rectangle, with its diameter equal to the width of the rectangle, which is 6 cm.

**Steps to calculate the perimeter:**
1. **Perimeter of the rectangle (excluding the side attached to the semicircle):**
   - \( P_{\text{rectangle}} = 6 \, \text{cm} + 4 \, \text{cm} + 4 \, \text{cm} = 14 \, \text{cm} \) (we exclude the top side)
   
2. **Circumference of the semicircle:**
   - The diameter is 6 cm, so the radius \( r = \frac{6}{2} = 3 \, \text{cm} \).
   - Circumference of a full circle is \( 2\pi r \), so the circumference of the semicircle is \( \pi r = \pi \times 3 \, \text{cm} = 3\pi \, \text{cm} \).

3. **Total Perimeter:**
   - \( P_{\text{total}} = 14 \, \text{cm} + 3\pi \, \text{cm} \).
   - The exact perimeter is \( 14 + 3\pi \) cm.

### (b) Second Composite Shape:
This shape is a rectangle with a semicircle on one side.

- **Rectangle:** The rectangle has a width of 5 cm and a height of 2 cm.
- **Semicircle:** The semicircle is attached to the top of the rectangle, with its diameter equal to the width of the rectangle, which is 5 cm.

**Steps to calculate the perimeter:**
1. **Perimeter of the rectangle (excluding the side attached to the semicircle):**
   - \( P_{\text{rectangle}} = 5 \, \text{cm} + 2 \, \text{cm} + 2 \, \text{cm} = 9 \, \text{cm} \) (we exclude the top side)

2. **Circumference of the semicircle:**
   - The diameter is 5 cm, so the radius \( r = \frac{5}{2} = 2.5 \, \text{cm} \).
   - Circumference of a full circle is \( 2\pi r \), so the circumference of the semicircle is \( \pi r = \pi \times 2.5 \, \text{cm} = 2.5\pi \, \text{cm} \).

3. **Total Perimeter:**
   - \( P_{\text{total}} = 9 \, \text{cm} + 2.5\pi \, \text{cm} \).
   - The exact perimeter is \( 9 + 2.5\pi \) cm.

### Summary of Results:
- For the first shape (a), the exact perimeter is \( 14 + 3\pi \) cm.
- For the second shape (b), the exact perimeter is \( 9 + 2.5\pi \) cm.

Would you like more details on these calculations, or do you have any other questions?

### Relative Questions:
1. What is the formula for the circumference of a full circle?
2. How would you find the area of these composite shapes instead of the perimeter?
3. Can you explain how the perimeter of a rectangle is generally calculated?
4. What is the significance of using exact values like \(\pi\) in these perimeter calculations?
5. How would the perimeter change if the shapes had a full circle instead of a semicircle?

### Tip:
When working with composite shapes, it's important to carefully consider which parts of the shape contribute to the total perimeter.

Learn how to calculate the exact perimeter of composite shapes composed of rectangles and semicircles. This problem covers geometry concepts including perimeter calculation, circumference of semicircles, and formula derivation for total perimeter. Suitable for Grades 7-9.

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