A circle is inscribed in a square of side 14 cm. Find the area enclosed between the square and the circle.

Answer

To find the area enclosed between the square and the inscribed circle, we can follow these steps:

### Step 1: Find the side length of the square.
The side length of the square is given as 14 cm.

### Step 2: Calculate the area of the square.
The area of a square is calculated using the formula:
\[ \text{Area of square} = \text{side}^2 \]
Substituting the side length:
\[ \text{Area of square} = 14^2 = 196 \text{ cm}^2 \]

### Step 3: Determine the radius of the inscribed circle.
Since the circle is inscribed in the square, the radius of the circle is half the side length of the square:
\[ \text{Radius} = \frac{\text{side}}{2} = \frac{14}{2} = 7 \text{ cm} \]

### Step 4: Calculate the area of the circle.
The area of a circle is calculated using the formula:
\[ \text{Area of circle} = \pi r^2 \]
Substituting the radius:
\[ \text{Area of circle} = \pi \times 7^2 = 49\pi \text{ cm}^2 \]

### Step 5: Find the area enclosed between the square and the circle.
To find the area between the square and the circle, we subtract the area of the circle from the area of the square:
\[ \text{Enclosed area} = \text{Area of square} - \text{Area of circle} \]
Substituting the values:
\[ \text{Enclosed area} = 196 - 49\pi \]

### Step 6: Substitute the value of \(\pi\) and calculate the enclosed area.
Using \(\pi \approx 3.14\):
\[ \text{Enclosed area} = 196 - 49 \times 3.14 \]
Calculating \(49 \times 3.14\):
\[ 49 \times 3.14 = 153.86 \]
Now substituting this back:
\[ \text{Enclosed area} = 196 - 153.86 = 42.14 \text{ cm}^2 \]

### Final Result:
The area enclosed between the square and the circle is approximately:
\[ \text{Enclosed area} \approx 42.14 \text{ cm}^2 \]