A square and a rectangle will meet the given criteria.
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a right triangle, a pentagon w/ a right angle, alot of shapes with right angles.
In a right prism, the lateral sides are perpendicular to the bases and so all of them are rectangular.In an oblique prism, the lateral sides are not perpendicular to the bases so that some of them (at least) are non-rectangular parallelograms.In a right prism, the lateral sides are perpendicular to the bases and so all of them are rectangular.In an oblique prism, the lateral sides are not perpendicular to the bases so that some of them (at least) are non-rectangular parallelograms.In a right prism, the lateral sides are perpendicular to the bases and so all of them are rectangular.In an oblique prism, the lateral sides are not perpendicular to the bases so that some of them (at least) are non-rectangular parallelograms.In a right prism, the lateral sides are perpendicular to the bases and so all of them are rectangular.In an oblique prism, the lateral sides are not perpendicular to the bases so that some of them (at least) are non-rectangular parallelograms.
For the perimeter, you just go round the shape, adding the lengths of each side as you go along. There may or may not be simple formulae of the area for a shape with unequal sides. If all you know is the [different] side lengths then only a triangle has a relatively simple formula for its area. If you also know that some of the sides are parallel, then you can find the area of a rectangle. Then, if you also know the perpendicular distance between the parallel sides, you can do a parallelogram. If, in addition you know which sides are parallel, a trapezium. And so on.
A polygon need not have ANY perpendicular or parallel lines. For example, consider an equilateral triangle. It can happen that two sides of a polygon, extended if necessary, meet at a point where they form a 90 degree angle. Those two lines are perpendicular. There may be pairs of lines such that, no matter how far you extend them in either direction, they will never meet. Such lines are parallel. A triangle cannot have parallel lines but it can have perpendicular lines. Any polygon of 4 or more sides can have sides that are perpendicular or parallel (or some of each).
Any polygon must have at least three sides. So a shape with only one pair of adjacent sides must be lenticular (shaped like a lens) else it is some very odd shape.