On a square cardboard sheet of area `784 cm^(2)` , four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square not covered by the circular plates.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the side length of the square cardboard sheet.
Given the area of the square cardboard sheet is \(784 \, \text{cm}^2\).

The formula for the area of a square is:
\[
\text{Area} = \text{side}^2
...