To find the area of the given composite shape, I will break it into simpler shapes and calculate the area of each part separately:

Step-by-step solution:

1. Divide the shape into components:

   • A semicircle (top left).
   • A rectangle (bottom middle).
   • A right triangle (right side).

2. Calculate the area of each shape:

   • Semicircle: The diameter is 4 cm, so the radius $r = \frac{4}{2} = 2$ cm. The area of a full circle is $\pi r^2$, so the area of the semicircle is: $\text{Area of semicircle} = \frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi (4) \approx \frac{1}{2} \times 12.57 = 6.28 \, \text{cm}^2$

   • Rectangle: The width is 4 cm and the height is 2 cm. $\text{Area of rectangle} = 4 \times 2 = 8 \, \text{cm}^2$

   • Right triangle: The base is 5 cm and the height is 2 cm. $\text{Area of triangle} = \frac{1}{2} \times 5 \times 2 = \frac{1}{2} \times 10 = 5 \, \text{cm}^2$

3. Total area: Add the areas of all three parts: $\text{Total area} = 6.28 + 8 + 5 = 19.28 \, \text{cm}^2$

The closest correct choice is 19.79 cm².

Would you like more explanation on any part of the solution?

Related Questions:

1. How do you find the area of composite shapes with different curves?
2. What are other ways to calculate the area of a triangle with different dimensions?
3. How can you approximate the value of π more accurately?
4. What techniques can simplify complex area calculations?
5. What are common mistakes when finding areas of composite shapes?

Tip: Always break down complex shapes into simpler parts to make calculations easier.