To find the area of the given shape, we will divide it into simpler geometric parts, calculate their areas, and sum them up.

Step 1: Divide the shape

1. The shape can be divided into:
   • A quarter-circle (top-left curved section)
   • A rectangle (central section)
   • A triangle (right triangular section)

Step 2: Calculate the areas

1. Quarter-circle area:

   • Radius = $4 \, \text{cm}$
   • Area of a full circle = $\pi r^2 = \pi (4)^2 = 16\pi$
   • Quarter-circle area = $\frac{1}{4} \times 16\pi = 4\pi \approx 12.57 \, \text{cm}^2$

2. Rectangle area:

   • Width = $4 \, \text{cm}$
   • Height = $2 \, \text{cm}$
   • Area = $4 \times 2 = 8 \, \text{cm}^2$

3. Triangle area:

   • Base = $5 \, \text{cm}$
   • Height = $2 \, \text{cm}$
   • Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 2 = 5 \, \text{cm}^2$

Step 3: Add the areas

Total area = Quarter-circle area + Rectangle area + Triangle area
$\text{Total area} = 12.57 + 8 + 5 = 25.57 \, \text{cm}^2$

Final Answer:

The area of the shape is 25.57 cm².

Would you like me to elaborate on any step?
Here are some related questions to consider:

1. How do you calculate the area of a full circle versus a quarter-circle?
2. What are other examples of dividing irregular shapes into simpler parts?
3. How does the Pythagorean theorem help in composite area problems?
4. Can you use integration to verify the area of curved shapes?
5. How do you estimate errors in area calculations when approximating $\pi$?

Tip: Always sketch the divisions for composite shapes; it ensures all parts are accounted for.