If you know the length of the side, multiply it by the square root of 2.
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Divide the length of the diagonal of a square by 1.4142 (which is the square root of 2) to find the length of a side. Similarly, to find the length of the diagonal of a square, multiply the length of a side by 1.4142.
Square the diagonal and take away the square of width, this gives you the square of the other side. Add the square root of the two sides and multiply by two.
Diagonal of a rectangle or square = square root of ( length2 + width2 )
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
Ah, the diagonal of a square is a special thing indeed. If you have a square that's 18 units on each side, you can use a little math magic to find its diagonal. By using the Pythagorean theorem, you'll see that the diagonal of this square would be 18 times the square root of 2. Just remember, there's always a way to find beauty and harmony in even the most geometric of shapes.