Polygons are either convex or concave. A polygon is convex if each of its interior angles measures less than 180°; otherwise it is concave. They are sometimes called convex and concave shapes — polygons are shapes that are closed, two-dimensional, and made of straight (not curved) lines.
Quadrilaterals are simply polygons with four sides, thus the same definitions apply. A convex quadrilateral is a four-sided polygon whose interior angles all measure less than 180°. A four-sided polygon that has an interior angle over 180° is considered a concave quadrilateral.
A regular polygon is a polygon that is equilateral (all sides have the same length) and equiangular (all angles are equal in measure). Since the angles of regular polygons have to be equal, it is impossible for them to be over 180° — for that reason, all regular polygons are convex.
Check out the Montessori-inspired resources available here for free.