Let Q be a convex region in R2 and let L be a line segment of length I that connects points on the boundary of Q. As we move one end of L around the boundary, the other end Will also move about this boundary, and the midpoint of L will trace out a curve Within Q that bounds a (smaller) region F. Using the corolla to Green's Theorem for nding area, nd an expression that relates the area of F to the area of Q in terms of the length I of the line segment. [You might start with some simple regions, but you must show this generally]