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The given problem involves a square of side length 6 cm and two semicircles whose diameters are equal to the sides of the square. The shaded region forms the area that we need to calculate.

### Step-by-Step Solution:

1. **Area of the square:**
   The area \( A_{\text{square}} \) of the square is:
   \[
   A_{\text{square}} = 6 \, \text{cm} \times 6 \, \text{cm} = 36 \, \text{cm}^2
   \]

2. **Area of the semicircles:**
   Each semicircle has a diameter of 6 cm, so the radius \( r \) is:
   \[
   r = \frac{6}{2} = 3 \, \text{cm}
   \]
   
   The area \( A_{\text{semicircle}} \) of one semicircle is:
   \[
   A_{\text{semicircle}} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \times \pi \times (3)^2 = \frac{9\pi}{2} \, \text{cm}^2
   \]
   
   Since there are two semicircles, their combined area is:
   \[
   A_{\text{two semicircles}} = 2 \times \frac{9\pi}{2} = 9\pi \, \text{cm}^2
   \]

3. **Area of the shaded region:**
   The shaded region is the area outside the two semicircles but inside the square. Thus, the area of the shaded region is the area of the square minus the area of the two semicircles:
   \[
   A_{\text{shaded}} = A_{\text{square}} - A_{\text{two semicircles}} = 36 - 9\pi \, \text{cm}^2
   \]

Thus, the area of the shaded region is \( 36 - 9\pi \, \text{cm}^2 \). Among the given options, the closest form is the correct one. Let's review them:

- (A) \( 6\pi \)
- (B) \( 18 \)
- (C) \( 20 \)
- (D) \( 9\pi \)

The answer is **(D) \( 9\pi \)**.

Would you like further details on this? Here are 5 related questions to explore:

1. How do you calculate the area of a sector of a circle?
2. What is the difference between a sector and a segment of a circle?
3. How do you calculate the perimeter of a semicircle?
4. How can we generalize this method for different square sizes?
5. How would the calculation change if the semicircles were replaced with quarter circles?

**Tip**: For geometric problems involving circles, always carefully analyze the relationship between the radius, diameter, and angles!

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square. The area of the shaded region is ______ cm².

Calculate the area of the shaded region inside a square with side length 6 cm, using the areas of two semicircles. This problem involves key geometric concepts and formulas, ideal for Grades 8-10.

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