Q:

how to set backroundcolor

Is there a way to set a common Backgroundcolor for all the tabs in a given TabBar?
Rightnow I am able to set color only for selected tabs using 

tabBar.getChildAt and setStyle

A:

Give them all a common styleName and set the backgroundColor style in CSS.
MXML
<mx:TabNavigator width="100%" height="100%">
    <mx:VBox label="Tab 1" styleName="tabContainers"></mx:VBox>
    <mx:VBox label="Tab 2" styleName="tabContainers"></mx:VBox>
    <mx:VBox label="Tab 2" styleName="tabContainers"></mx:VBox>
</mx:TabNavigator>

CSS:
.tabContainers
{
    backgroundColor: #ff0000;
}

