This is a geometric problem involving areas of circles or semicircles. Let’s analyze it step by step.

Problem Breakdown:

1. The figure consists of a large semicircle on top and two smaller semicircles below it.
2. The two smaller semicircles are inscribed within the larger semicircle.
3. The given dimensions are:
   • Diameter of each smaller semicircle = 7 cm.
   • Total diameter of the larger semicircle = 7 cm + 7 cm = 14 cm.
4. We need to calculate the shaded area (area of the larger semicircle minus the areas of the two smaller semicircles).

Step-by-Step Solution:

Step 1: Calculate the radius of each circle.

• Radius of the larger semicircle:
  $R = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{cm}.$
• Radius of each smaller semicircle:
  $r = \frac{\text{Diameter}}{2} = \frac{7}{2} = 3.5 \, \text{cm}.$

Step 2: Find the area of the larger semicircle.

The formula for the area of a semicircle is: $\text{Area of a semicircle} = \frac{\pi R^2}{2}.$ For the larger semicircle: $\text{Area}_{\text{large}} = \frac{\pi (7)^2}{2} = \frac{3.14 \times 49}{2} = \frac{153.86}{2} = 76.93 \, \text{cm}^2.$

Step 3: Find the area of one smaller semicircle.

Using the same formula: $\text{Area}_{\text{small}} = \frac{\pi r^2}{2}.$ For one smaller semicircle: $\text{Area}_{\text{small}} = \frac{\pi (3.5)^2}{2} = \frac{3.14 \times 12.25}{2} = \frac{38.465}{2} = 19.2325 \, \text{cm}^2.$

Step 4: Find the total area of the two smaller semicircles.

$\text{Total area of smaller semicircles} = 2 \times \text{Area}_{\text{small}} = 2 \times 19.2325 = 38.465 \, \text{cm}^2.$

Step 5: Calculate the shaded area.

The shaded area is the difference between the area of the larger semicircle and the total area of the two smaller semicircles: $\text{Shaded area} = \text{Area}_{\text{large}} - \text{Total area of smaller semicircles}.$ $\text{Shaded area} = 76.93 - 38.465 = 38.465 \, \text{cm}^2.$

Final Answer:

The shaded area is: $\boxed{38.47 \, \text{cm}^2}$

Would you like further clarification, or do you want to explore other problems? Here are some related questions to consider:

1. What is the total area of all the semicircles combined?
2. How would the shaded area change if the smaller semicircles had different diameters?
3. What is the perimeter of the shaded region (arc lengths)?
4. How would this calculation change if the larger semicircle were a full circle?
5. Can you calculate the area using a different method (e.g., subtracting from the full circle)?

Tip: Always ensure that the radii of semicircles are correctly identified before substituting into formulas!