Any regular polygons with an even number of sides can have opposite sides equal and parallel.
For quadrilaterals, if any two sides are equal and parallel, the other two sides must also be equal and parallel, and it is a parallelogram (square or rhombus). If the equal sides are not parallel, the figure is a trapezoid (UK trapezium).
a rectangle
2-dimensional figures. Four straight sides. Four angles that add to 360 degrees. Parallel opposite sides. Equal opposite sides. Equal opposite angles. Bisecting diagonals.
An equilateral shape would have equal and opposite sides.
Opposite sides are parallel; opposite sides are equal; opposite angles are equal.
The description given fits that of a square or a rhombus
The description fits a square or a rhombus. In a square, all sides are of equal length, opposite sides are parallel, and all angles are equal (90 degrees). In a rhombus, all sides are also of equal length and opposite sides are parallel, but the angles are not necessarily equal, as they can vary while remaining equal in opposite pairs.
paramid
Rectangle
opposite the smaller sides are equal and opposite the bigger sides are equal.
A parallelogram has opposite equal parallel sides
it may be a parallelogram or a kite both have opposite sides equal
equilateral is all equal sides so the opposite would be scalene: no equal sides