A surveyor wishes to lay out a square region with each side having length L. However, because of a measurement error, he instead lays out a rectangle in which the north-south sides both have length X and the east-west sides both have length Y. Suppose that X and Y are independent and that each is uniformly distributed on the interval [L - A, L + A] (where 0 < A < L). What is the expected area of the resulting rectangle?