The only thing that can be said is that the quadrilateral will have an area that is smaller than the square. The exact value depends on the location of the vertices.
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Quadrilateral
A square will. The only shape that can enclose more area with the same perimeter is a circle.
The area of the quadrilateral.
You cannot. A square can be distorted into a rhombus without changing the lengths of any of the sides, but with a different area. Similarly, the shape of any quadrilateral can be altered without affecting the length of its sides but changing its area.
Look in your math book. Square = side^2, parallelogram = base*height, etc.