Can some one please tell me why this is not working, I m using SharePoint online
On second line I m referring to the custom css.

CSS
<style type="text/css">
#DeltaPlaceHolderSearchArea {
display: none;
}
</style>
Don't do this. You can easily add a reference to a new css without editing the master page. There is a property on the web object called AlternateCSSUrl that can be set to ref your css. Use it instead. This will give you a start: Setting AlternateCssUrl in all subsites
As mentioned in the comments, you can reference css files using link tags or using SharePoint:CssRegistration as below:
<link rel="stylesheet" type="text/css" href="/_catalogs/masterpage/Style Library/customcss.css" />
or
<SharePoint:CssRegistration name="<% $SPUrl:~SiteCollection/_catalogs/masterpage/Style Library/customcss.css%>" after="corev15.css" runat="server"/>
When you use CssRegistration along with the ~SiteCollection token, SharePoint will convert it to the correct site collection URL and render it on the page.
<link rel="stylesheet" type="text/css" href="/_catalogs/masterpage/Style Library/customcss.css" />or<SharePoint:CssRegistration name="<% $SPUrl:~SiteCollection/_catalogs/masterpage/Style Library/customcss.css%>" after="corev15.css" runat="server"/>?