Each side of a square park is 80 m. At each corner of the park there is a flower bed in the form of a quadrant of a circle of radius 14 m, as shown in the figure. Find the area of the remaining part of the park.

Answer

To solve the problem step by step, we will calculate the area of the square park and then subtract the area of the flower beds (quadrants of circles) from it.

### Step 1: Calculate the area of the square park
The formula for the area of a square is:
\[ \text{Area} = \text{side}^2 \]
Given that each side of the square park is 80 m:
\[ \text{Area} = 80 \times 80 = 6400 \, \text{m}^2 \]

### Step 2: Calculate the area of one quadrant of a circle
The formula for the area of a full circle is:
\[ \text{Area} = \pi r^2 \]
Since we have a quadrant (which is one-fourth of a circle), the area of one quadrant is:
\[ \text{Area of one quadrant} = \frac{1}{4} \pi r^2 \]
Given that the radius \( r \) is 14 m:
\[ \text{Area of one quadrant} = \frac{1}{4} \times \frac{22}{7} \times (14)^2 \]
Calculating \( (14)^2 \):
\[ (14)^2 = 196 \]
Now substituting this into the equation:
\[ \text{Area of one quadrant} = \frac{1}{4} \times \frac{22}{7} \times 196 \]
Calculating further:
\[ = \frac{22 \times 196}{4 \times 7} \]
\[ = \frac{22 \times 196}{28} \]
Now simplifying \( \frac{196}{28} = 7 \):
\[ = 22 \times 7 = 154 \, \text{m}^2 \]

### Step 3: Calculate the area of four quadrants
Since there are four corners, we multiply the area of one quadrant by 4:
\[ \text{Area of four quadrants} = 4 \times 154 = 616 \, \text{m}^2 \]

### Step 4: Calculate the area of the remaining part of the park
To find the area of the remaining part of the park, we subtract the area of the flower beds from the area of the square park:
\[ \text{Area of remaining part} = \text{Area of square} - \text{Area of four quadrants} \]
\[ = 6400 - 616 = 5784 \, \text{m}^2 \]

### Final Answer
The area of the remaining part of the park is:
\[ \boxed{5784 \, \text{m}^2} \]