Let ω be a convex region in r2 and let l be a line segment of length i that connects points on the boundary of ω. 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 ω that bounds a (smaller) region γ. using the corollary to green’s theorem for finding area, find an expression that relates the area of γ to the area of ω in terms of the length i of the line segment.