That is not TwentyTwelve theme or a child theme of it. That’s a child theme of Responsive theme. But anyway WP standard body_class()
could be used to target certain element within specific page.
Not sure if Responsive Theme uses body_class()
in the <body>
but I think it does.
http://codex.wordpress.org/Function_Reference/body_class
Example
.home.page .widget-wrapper { background: red; }
The above will only affect widget in front home page.
Yes, you’re right – it is Responsive – sorry …thinking of another site. I will look into the body_class.