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We are tasked with finding the area of the shaded region in the given diagram, where:

- \( ABC \) is a quadrant of a circle with a radius of 28 cm.
- A semicircle is drawn with \( BC \) as its diameter.

### Steps to solve:
1. **Area of the quadrant \( ABC \)**:
   The quadrant is one-fourth of a circle with radius 28 cm. The area of a full circle is given by:
   \[
   \text{Area of the full circle} = \pi r^2 = \pi (28)^2 = 784\pi \, \text{cm}^2
   \]
   So, the area of the quadrant is:
   \[
   \text{Area of the quadrant} = \frac{1}{4} \times 784\pi = 196\pi \, \text{cm}^2
   \]

2. **Length of \( BC \) (Diameter of the semicircle)**:
   Since \( BC \) is the radius of the quadrant, its length is equal to the radius, which is 28 cm. Therefore, \( BC \) is the diameter of the semicircle, and the radius of the semicircle is:
   \[
   r_{\text{semicircle}} = \frac{28}{2} = 14 \, \text{cm}
   \]

3. **Area of the semicircle**:
   The area of a full circle with radius 14 cm is:
   \[
   \text{Area of the full circle} = \pi (14)^2 = 196\pi \, \text{cm}^2
   \]
   Therefore, the area of the semicircle is:
   \[
   \text{Area of the semicircle} = \frac{1}{2} \times 196\pi = 98\pi \, \text{cm}^2
   \]

4. **Area of the shaded region**:
   The shaded region is the difference between the area of the quadrant and the area of the semicircle:
   \[
   \text{Area of the shaded region} = 196\pi - 98\pi = 98\pi \, \text{cm}^2
   \]

Thus, the area of the shaded region is:
\[
\boxed{98\pi \, \text{cm}^2} \approx 307.88 \, \text{cm}^2
\]

Would you like further details or have any questions? Here are some related questions:

1. How do you find the area of a segment of a circle?
2. What is the formula for the circumference of a circle?
3. How do we calculate the perimeter of the shaded region?
4. How can we compute the area of irregular shapes?
5. What is the relationship between arc length and the area of a sector?

**Tip**: Always ensure the correct use of formulas for circle sectors and segments by double-checking whether the shape is a full circle, semicircle, or quadrant.

In the adjoining figure, ABC is a quadrant of a circle of radius 28cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Learn how to find the area of a shaded region formed by a quadrant and a semicircle, both sharing a common diameter, using circle geometry formulas. This guide covers detailed steps using the area formulas for circles, quadrants, and semicircles.

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