The diagram is not exact but you can follow from it:
The area of largest sector that can be inscribed in a square will be one vertex of the square as the centre of the sector and the side of square as it's radius.
According to the question:
required area will be=area of squareABCD-area of sector ADFEBA.
Now area of square =side^2=24^2=576sq.cm
Area of the sector=(1/4)*pi*radius^2
therefore area of cardboard wasted=area of the square -area of the sector