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The side lengths of a quadrilateral do not uniquely identify the shape, because a quadrilateral is not a rigid shape. It can be flexed so that its area can be varied without changing the side lengths.

As an example, consider a rectangle. It can be flexed into a parallelogram which can be made so thin that its area can be made smaller than any given value. Whereas a general quadrilateral may have a residual triangle that cannot be removed, there is a huge range of values for the area.

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12y ago

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