The length of the diagonal of a square is

(b) 100 cm2

A diagonal of a square forms the hypotenuse of a right-angled triangle with base and height equal to side a.

Diagonal $^{2}=a^{2}+a^{2}$

$\Rightarrow$ Diagonal $^{2}=2 a^{2}$

$\Rightarrow a=\frac{1}{\sqrt{2}}$ Diagonal

$=\frac{1}{\sqrt{2}} \times 10 \sqrt{2}$

$=10 \mathrm{~cm}$

$\therefore$ Area of the square $=a^{2}=10 \times 10=100 \mathrm{~cm}^{2}$