Let ABCD be the inscribed square whose side is x units.
Length of diagonal of square =AC=2a=√2×side ⇒x=
2a
√2
=√2a Therefore, area of inner square ⇒x2=(√2a)2=2a2 Side of the outer square =PQ=a+a=2a Therefore, area of outer square =(2a)2=4a2 Difference between the areas of the outer square and inner square =4a2−2a2=2a2