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)

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