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 parallelogram is a four sided shape where opposite sides are parallel and equal lengths. If you mean that ALL sides are equal lengths, you are looking for a rhombus.
A trapezium does not have to have adjacent sides equal, but might have. In the US, trapezium just means any old four-sided shape. Outside the US, it means a shape with at least two parallel sides.
Equilateral triangle.
trapezoid
rectangle
Not necessarily.
If it has four equal sides, then two parallel sides implies two PAIRS of parallel sides. The shape is a rhombus.
A parallelogram is a four sided shape where opposite sides are parallel and equal lengths. If you mean that ALL sides are equal lengths, you are looking for a rhombus.
A trapezium does not have to have adjacent sides equal, but might have. In the US, trapezium just means any old four-sided shape. Outside the US, it means a shape with at least two parallel sides.
Equilateral triangle.
trapezoid
trapezium
rectangle
an perticulogram
a rhombusNotice that if all 4 sides are equal, then they must be parallel.
Kite
The shape has to be a parallelogram since it has no lines of symmetry and all sides are equal and parallel