A quadrilateral is a flat shape, in one plane, defined by four points at the four corners. A quadrilateral has four sides that can be of any length, and four corners, that can be any angle so long as they add up to 360 degrees. A rectangle is a special kind of quadrilateral, and a square is a special kind of rectangle.
To figure out the perimeter of the quadrilateral, you can add the lengths of all the sides together. To figure out the area of a quadrilateral, you have to cut it into shapes that are easier to figure out. You cut it into two pieces running a line from one corner to the opposite corner, and then you have two triangles. You can figure out the area of those triangles and then add them together to get the area of your quadrilateral. But unless at least two opposite sides of the quadrilateral are parallel to each other, it's hard to figure out the height of the triangles, so you won't really be able to figure out the area of the quadrilateral either. If they are parallel, then you have a parallelogram, which is easier to figure out.