A quadrilateral is a parallelogram with four sides. For example: square, rectangle, parallelogram, trapezoid, rhombus, diamond...
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All of them.
square and rhombus i think
You can make any triangle, quadrilateral or pentagon with three suitable triangles.
Actually, it depends on the kite maker. It may be quadrilateral in shape, as you asked. It can also be square. It can be a triangle, like the Chinese make it, or it can be any fancy shape.