(i) a quadrilateral?

A square is a quadrilateral because it has four equal sides.

(ii) a parallelogram?

A square is a parallelogram since it has opposite sides equal and parallel.

(iii) a rhombus?

A square is a rhombus because it has all four sides of equal length.

(iv) a rectangle?

A square is a rectangle because its opposite sides are equal and parallel and each angle is right angle.