Consider a convex n-gon A_{1} A_{2} \cdots A_{n}. (Note: In a convex polygon, all interior angles are less than 180^{\circ}.) Let h be a positive number. Using the sides of the polygon as bases, we draw n rectangles, each of height h, so that each rectangle is either entirely inside the n-gon or partially overlaps the inside of the n-gon.
As an example, the left figure below shows a pentagon with a correct configuration of rectangles, while the right figure shows an incorrect configuration of rectangles (since some of the rectangles do not overlap with the pentagon):
(a) Correct
Incorrect
Prove that it is always possible to choose the number h so that the rectangles completely cover the interior of the n-gon and the total area of the rectangles is no more than twice the area of the n-gon.