Presuming our geometry is Euclidean, such a shape would be a rectangle, since all 4 angles would be right angles.
If our geometry is hyperbolic, it would be possible to construct such a quadrilateral which is not a rectangle (and in fact, rectangles cannot exist in a hyperbolic geometry). I do not believe such a quadrilateral has any special name.
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A square is a four-sided shape with all sides equal and all angles equal.
No shape has four equal sides and four different angles - either there are two pairs of equal angles, or all four angles are the same; or all sides are not the same length.
A parallelogram.
square
A shape with six sides is a hexagon. A hexagon with all sides and angles equal is a regular hexagon.