Let's break this problem down step by step:

Step 1: Identify the shapes

The compound shape consists of:

1. A rectangle with dimensions:
   • Width = 4 cm
   • Height = 16 cm
2. A semicircle with:
   • Diameter = 4 cm (same as the rectangle’s width)
   • Radius = 4 cm ÷ 2 = 2 cm

Step 2: Calculate the area of the rectangle

$\text{Area of rectangle} = \text{width} \times \text{height}$ $= 4 \times 16 = 64 \text{ cm}^2$

Step 3: Calculate the area of the semicircle

The area of a full circle is: $\pi r^2$ Since we have a semicircle, we divide by 2: $\text{Area of semicircle} = \frac{1}{2} \pi r^2$ $= \frac{1}{2} \times \pi \times 2^2$ $= \frac{1}{2} \times \pi \times 4$ $= \frac{4\pi}{2} = 2\pi$

Approximating $\pi$ as 3.1416: $\text{Area of semicircle} \approx 2 \times 3.1416 = 6.2832 \text{ cm}^2$

Step 4: Calculate the total area

$\text{Total Area} = \text{Area of rectangle} + \text{Area of semicircle}$ $= 64 + 6.2832$ $= 70.2832$

Step 5: Round to 1 decimal place

$\mathbf{70.3 \text{ cm}^2}$

Final Answer:

$\boxed{70.3 \text{ cm}^2}$

Would you like me to explain any step further?

Related Questions:

1. How do you find the perimeter of this compound shape?
2. What would the total area be if the semicircle was a full circle instead?
3. How would the area change if the width of the rectangle were doubled?
4. What is the ratio of the semicircle’s area to the rectangle’s area?
5. How can this problem be applied in real-world construction or design?

Tip: Always check if the given shape consists of familiar geometric figures before solving for area or perimeter!