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There are many, many quadrilaterals used in real life.
Square-like shapes are often used for uniformity: they are easy to tesselate, or pattern with. Same with diamonds or rectangles.
Shapes like trapeziums: with a wide base and a narrower top, are used for construction or building.
Shapes such as rhombuses or other irregular quadrilaterals (pictured below) are used for design: to make things look good, add something the eye notices because it is not uniform.
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