a Quadrilateral
"...need to be the same SIZE?" Quadrilateral (including trapezium).
a polygon with 4 right angles and 4 sides of the same length
square
a polygon
A quadrilateral
There are infinitely many such shapes. A polygon with 4 or more sides can have two sides that are parallel and they need not be the same length.
a quadrilateral
A square.
A trapezoid or a trapezium
rhombus
A quadrilateral