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.