Welcome to CF!
This is an over-complicated way that can be applied to different scenarios. I dont know how useful it will be though..
You can do it with two backgrounds. One that is attached to the <body> and one that is attached to the div#apDiv1.
This method also guarantees that someone who does have a resolution over 2000px still gets a complete header.
Repeat the green part down the x-axis.
background:url("green-part") repeat-x top;}
Then the div#apDiv1 can center the black part over the green part.
background:url("black-part") center top no-repeat;
margin:0 auto; <---centers
width:1000px; <---new width for the black part