Find the area of a square with a diagonal of 4cm.

Let the side length be s. Then sqrt (s^2+s^2) is the length of the diagonal.

sqrt (2s^2) = 4 cm, so 2s^2 = 16 cm, and s^2 = 8, so that s = 2sqrt (2).

The area of this square is s^2, which here is 4 (2), or 8 square units (answer)