Connected area is that little bit of the dropdown for a menu where the border is discontinuous. Below is an examples of how to access and paint that.

protected override void OnRenderToolStripBorder(ToolStripRenderEventArgs e)
{
    using (Brush b = new SolidBrush(ColorTable.MyBackgroundColor))
    {
        e.Graphics.FillRectangle(b, e.ConnectedArea);
    }
}