Código HTML:
<html>
<head>
<title> New Document </title>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1" />
<STYLE type="text/css">
<!--
.estilouno{background-color:green;}
.estilodos{background-color:red;}
-->
</STYLE>
<script language="javascript">
<!--
function nombre(obj){
if (obj) document.getElementById("tarea").className="estilouno";
else document.getElementById("tarea").className="estilodos";
return true;
}
//-->
</script>
</head>
<body>
<input type="radio" name="radio" id="radio" value="1" checked="false" onclick="nombre(false)">Radio1</input>
<input type="radio" name="radio" id="radio" value="2" onclick="nombre(true)">radio2</input>
<textarea name="tarea" id="tarea" rows="20" cols="10">precioso</textarea>
</body>
</html>