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A trapezoid is not a parallelogram but they are both 4 sided quadrilaterals.
it is a shape but it depends what type of shape you are looking for example and equalateral triangle, or an equalateral parelleogram.
It is an inscribed quadrilateral or cyclic quadrilateral.
It is simply a quadrilateral - there is no special name for such a quadrilateral.
It is an arrowhead quadrilateral