https://file.aiquickdraw.com/mathbot/file/1725087912656w5ykvvif.jpg

The image contains a composite shape made up of a rectangle with a semicircle on top. The dimensions given are:
- Height of the rectangle: 17 cm
- Width of the rectangle (and the diameter of the semicircle): 28 cm

### (a) **Perimeter Calculation:**

The perimeter of this shape consists of:
1. The two sides of the rectangle (2 × 17 cm).
2. The width of the rectangle (28 cm).
3. The curved part of the semicircle (half the circumference of a full circle).

The formula for the circumference of a full circle is \( C = \pi d \), where \( d \) is the diameter. For the semicircle, the perimeter is half of that:
\[ \text{Curved part of semicircle} = \frac{1}{2} \times \pi \times 28 \text{ cm} = 14\pi \text{ cm} \]

So, the total perimeter \( P \) is:
\[
P = 2 \times 17 \text{ cm} + 28 \text{ cm} + 14\pi \text{ cm}
\]
\[
P = 34 \text{ cm} + 28 \text{ cm} + 14\pi \text{ cm}
\]
\[
P = 62 \text{ cm} + 14\pi \text{ cm} \approx 62 \text{ cm} + 43.96 \text{ cm} \approx 105.96 \text{ cm}
\]

### (b) **Area Calculation:**

The area of the composite shape consists of:
1. The area of the rectangle.
2. The area of the semicircle.

**1. Area of the rectangle:**
\[ A_{\text{rectangle}} = \text{length} \times \text{width} = 28 \text{ cm} \times 17 \text{ cm} = 476 \text{ cm}^2 \]

**2. Area of the semicircle:**
The area of a full circle is \( A = \pi r^2 \), where \( r \) is the radius. Since the diameter is 28 cm, the radius \( r \) is \( 14 \) cm. The area of the semicircle is half of the full circle's area:
\[ A_{\text{semicircle}} = \frac{1}{2} \times \pi \times 14^2 \text{ cm}^2 \]
\[ A_{\text{semicircle}} = \frac{1}{2} \times \pi \times 196 \text{ cm}^2 = 98\pi \text{ cm}^2 \approx 307.88 \text{ cm}^2 \]

**Total area \( A \) is:**
\[
A = 476 \text{ cm}^2 + 98\pi \text{ cm}^2 \approx 476 \text{ cm}^2 + 307.88 \text{ cm}^2 \approx 783.88 \text{ cm}^2
\]

### Final Answers:
- **Perimeter:** \( \approx 105.96 \text{ cm} \)
- **Area:** \( \approx 783.88 \text{ cm}^2 \)

Do you want more details, or have any questions?

**Related Questions:**
1. How would the perimeter change if the diameter of the semicircle were increased?
2. What if the rectangle had a different height? How would that affect the area?
3. How is the formula for the circumference of a circle derived?
4. How would the calculations change if the shape was a quarter circle instead of a semicircle?
5. Can the shape be split in another way to make the calculations simpler?

**Tip:** For composite shapes, always break them down into simpler components to calculate area and perimeter.

Learn how to calculate the perimeter and area of a composite shape consisting of a rectangle and a semicircle. Detailed step-by-step solution provided with formulas for perimeter and area calculations. Suitable for Grades 7-9 students studying geometry.

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