Well, I think and as far as I know, pentagon has 5 sides/angles/edges, then quadralatral (from the term quad/ quatro) so meaning four, so pentagon is not a quadralatral. ok!
A quadrilateral is a polygon with four sides. The sides can be of any lengths, so there are many possible shapes. The angles do not even have to be all convex, I think, so you make a heart-shape with pointy angles-- ie 2 V's joined, one under the other. Of course, squares, oblongs, kites, trapezoids and rhombi are all quadrilaterals.