Barbara $($her friends call her Barb because she solves problems about wire$)$ is planning a sustainable fish farm venture for her large property. She has a total of $640$ meters of wire for the electrified fencing which will be used to enclose two unconnected pool areas. One of the areas must be square, while the other must be a rectangle that is two times as long as it is wide. The square pond enclosure must contain at least $100$ square meters and the other one $($the rectangle$)$ at least $512$ square meters. Find the maximum total area of the two enclosures