The length of the diagonal of a square is 10 . What is the area of this square?
Let the side length of the square be $s$.

Since the diagonal of length 10 is the hypotenuse of a right-angled triangle with two sides of the square as legs, then $s^{2}+s^{2}=10^{2}$ or $2 s^{2}=100$, which gives $s^{2}=50$.

Since the area of the square equals $s^{2}$, then the area is 50 .

ANSWER: 50