Once you account for squaring up and binding, you usually want at least an inch extra on side triangles and corners. Also cutting the side triangles like that is going to put the long side on the bias, making it a lot stretchier and harder to work with.
There's a good chance you'll loose some points doing it this way. If that really bothers you, then you might want to think about buying some more fabric and having the sides and corners be background.