问题

A surveyor wishes to lay out a square region with each side having length $L$. However, because of 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 the each is uniformly distributed on the interval $[L-A,L+A]$ (where $0 < A < L$). What is the expected area of the resulting rectangle?