To solve the problem of finding the shaded area in a square with an inscribed circle, follow these steps:

Step 1: Identify Key Dimensions

Assume the square has a side length ( s ). For an inscribed circle, the diameter of the circle equals the side length of the square (( d = s )), so the radius ( r = \frac{s}{2} ).

Step 2: Calculate Area of the Square

Area of square = ( s^2 ).

Suppose the square’s side length is 10 cm (a common value in such problems):
Area of square = ( 10^2 = 100 \, \text{cm}^2 ).

Step 3: Calculate Area of the Circle

Area of circle = ( \pi r^2 = \pi \left(\frac{s}{2}\right)^2 = \frac{\pi s^2}{4} ).

For ( s = 10 ):
Area of circle = ( \pi \times 5^2 = 25\pi \approx 78.5 \, \text{cm}^2 ).

Step 4: Find Shaded Area

If the shaded area is the part of the square not covered by the circle:
Shaded area = Area of square - Area of circle

( = 100 - 25\pi \approx 100 - 78.5 = 21.5 \, \text{cm}^2 ).

Answer: Approximately (\boxed{21.5}) (units depend on the given side length; if exact value is needed: (100 - 25\pi)).

(Note: Adjust the calculation if the square’s side length differs—replace (s) with the given value.)

(\boxed{21.5}) (assuming side length 10 cm)
Or exact value: (\boxed{100 - 25\pi}) (if required)

But if the side length was different (e.g., 8 cm: (\boxed{64 - 16\pi \approx 13.73})), but based on common problems, (\boxed{21.5}) is a typical result.

Final Answer
(\boxed{21.5}) (rounded to one decimal place) or (\boxed{100 - 25\pi}) (exact).

For simplicity, let's go with the numerical approximation:
(\boxed{21.5})

(\boxed{21.5})

作者声明:本文包含人工智能生成内容。