If the lengths of the sides of a square are halved, the area of the new square is

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The area of a square is equal to the length of one side of the square multiplied by itself. Therefore, if the length of a side of a square is x, the area of the square is x 2 . If the sides of the square are halved, then the area of the square becomes ( 1 ⁄ 2 x)( 1 ⁄ 2 x) = 1 ⁄ 4 x 2 . The area of the new square, 1 ⁄ 4 x 2 , is one-fourth the area of the old square, x 2 .

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