Covariance of two random variables distributed uniformly over a rectangle

Question

I am looking at problem 36 on page 76 of Leo Breiman's text entitled "Probability and Stochastic Processes, With a View Toward Applications, second edition," wherein the goal is to calculate the covariance of two random variables, $X$ and $Y$, both of which are uniformly distributed over a rectangle. The vertices of the rectangle are located at $(c,d)$, $(c,-d)$, $(-c,-d)$, and $(-c,d)$ where the long edges of the rectangle are parallel to the x-axes and $0\lt d \lt c$. Leo Breiman states the answer as: $$\Gamma_{X,Y} = \frac{1}{6}\left({c^2}-{d^2}\right).$$ In my attempt, I began by identifying the random variable $Y$ with the y-axes portion of the rectangle and the random variable $X$ with the x-axes portion of the rectangle. I then guessed at the form of the probability density function, I tried: $${x^2}-{y^2}, \text{(this form does not satisfy the conditions of a PDF)},$$ $${x^2}+{y^2},\text{and}$$ $${x^2}{y^2}.$$ Nothing worked. Has anyone out there worked this problem to completion and, if so, would you mind letting me know what the correct form of the PDF is to use. Thanks.