An outbox of a quadrilateral is a rectangle such that each vertex of the given quadrilateral lies on one side of the rectangle and different vertices lie on different sides. We first investigate those quadrilaterals whose every outbox is a square. Next, we consider the maximal outboxes of rectangles and those quadrilaterals with perpendicular diagonals. At last, we use the theorem from calculus to give the formula of the maximal area of outboxes of an arbitrary quadrilateral, this serves as a good example illustrating the applications of calculus. (Contains 7 figures.)