A square is of area 200 sq. m. A new square is formed in such a way that the length of its diagonal is $$\sqrt{2}$$  times of the diagonal of the given square. Then the area of the new square formed is

area of square = $$ side^2 = 200 $$

side a= $$ \sqrt{200} = 10 \sqrt{2} $$

diagonal = $$ \sqrt {2} a = \sqrt{2} \times 10 \times \sqrt{2} = 20 $$

A new square is formed in such a way that the length of its diagonal is $$\sqrt{2}$$ times of the diagonal of the given square

therefore diagonal of the new square = $$ \sqrt {2} \times 20 $$

$$ \sqrt{2} \times 20 = \sqrt {2} a $$

solving a = 20

therefore area of new square = $$ 20^2 = 400 $$