60. Exemplar exercise problems XXXVI

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 sheet not covered by the circular plates.

 

Area not covered by the circular plates \(=\) \(cm^2\)