How to change page CSS based on parent menu item?
If it is just additional classes you need, you can add additional and unique classes to menu items using the Menu CSS Names or Menu Attributes modules.

Or, you can effect the element of another DIV on hover using pure CSS like below...

HTML

&lt;a id="menu-item" href="#"&gt;Menu Item&lt;/a&gt;

&lt;div id="container"&gt;
    &lt;h1&gt;Change This Background&lt;/h1&gt;
&lt;/div&gt;


CSS

#container {
    background:blue;
}

#menu-item:hover + #container {
    background:red;
}


See Fiddle here... Affect Another Div on Hover