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The length of one side of a square with a 16-centimeter diagonal is: 11.31 cm
You don't - you need additional information. Many different rectangles can have the same diagonal. If you know the diagonal and one side (which must be LESS than the diagonal), you can use Pythagoras' Theorem to calculate the other side.
draw a straight line from one corner to its opposite corner the length of the diagonal is the length of one side times the square root of 2
Yes: The intersection is at one end of each side. This is true for a diagonal of any quadrilateral.
The diagonal multiplied by sin(angle) gives one side of the rectangle and the diagonal times cos(theta) gives the other. So the area is (diagonal)2 x cos(theta) x sin(theta).