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Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length).
so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units.
As a square has sides of equal length the square on one side is actually the area of the square.
i.e. the area of a square with a diagonal of 10 units is 50 square units.
or generically the area of a square with a diagonal of length 'x' = (x2)/2
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Check
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