Any rhombus definitely fits the description, and any polygon with
more than 4 sides ... regular or not ... can fit it too.
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a quadrilateral is a shape with four equal sides.
No, a parallelogram does not have perpendicular sides by definition. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Perpendicular sides would form a right angle, which is a characteristic of rectangles, squares, and other types of quadrilaterals, but not parallelograms.
A rhombic octagon. An ordinary regular octagon does have perpendicular sides. They do not meet in the outline of the octagon because they are alternate, but they are still perpendicular. However, in the same way that a rhombus is a distorted square, a rhombic octagon can have 4 pairs of parallel sides but no perpendicular ones.
The question asks about four sides and 2 perpendicular sides. That makes 6 sides in all. So it is a hexagon with either only one right angle, or two sides that are mutually perpendicular.