quadrilateral has perpendicular lines
Any polygon with four or more sides can have perpendicular and parallel lines.
If it's a regular polygon, and you know the length of the perpendicular from the center to the middle of a side, and the length of a side, A = LNS, where L is the length of the perpendicular, N is the number of sides, and S is the number of sides. See the link for a more detailed explanation of various ways to compute the area of regular polygons.
A polygon with 1,000 sides is known as a chiliagon. A hectogon is a polygon that has 100 sides, and a polygon with 8 sides is called an octagon.
The sides of a polygon are straight line boundaries of the polygon.
Apothem
No, a pentagon is a polygon with 5 sides.
infinite
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).
A polygon with four or more sides can meet these requirement.
Any regular polygon with 2k sides where k > 2. Also any such polygon that has been stretched in any directions parallel to its sides.
A shape that can have three pairs of perpendicular sides is a rectangular prism (or cuboid) when considering its three-dimensional form. Each pair of sides meets at right angles, creating a structure with three sets of perpendicular edges. In a two-dimensional context, no standard polygon can have three pairs of perpendicular sides, as it would require more than four sides, violating the definition of a polygon.
Any polygon with four or more sides can have perpendicular and parallel lines.
apothem
No
A polygon with only 1 pair of perpendicular sides is called a trapezoid. In a trapezoid, one pair of opposite sides are parallel, while the other pair are not parallel and intersect at a right angle. The sum of the interior angles of a trapezoid is always 360 degrees. Examples of trapezoids include isosceles trapezoids, right trapezoids, and scalene trapezoids.
TRAPEZOID
There are infinitely many possible answers. For example, any regular polygon with an even number of sides.