public void deleteArea() {
   Area__c record2Delete = [/*SOQL*/];
   delete record2Delete;
}

<apex:pageBlockSection title="Areas" columns="1" id="pbs" >

<apex:pageBlockTable  value="{!Area__c.Location_Areas__r}" var="item">
  <apex:column headerValue="Action">
 <a href="javascript:if (window.confirm('Are you sure? you want to delete - {!item.Location_Area__r.Name} ?')) deleteArea('{!item.Id}');" >Delete </a>
</apex:column>
  <apex:column headerValue="Area">
    <apex:outputLink value="{!URLFOR($Action.Area__c.View, item.Area__c)}">{!item.Area__c.Name}</apex:outputLink>
  </apex:column>

</apex:pageBlockTable>
</apex:pageBlockSection>

<apex:actionFunction action="{!deleteArea}" name="deleteArea" reRender="pbs">
 <apex:param name="selectedDelId" value="" assignTo="{!deleteAreaId }" />
</apex:actionFunction>

<apex:output panel id="panelId">
<apex:pageBlockTable  value="{!Area__c.Location_Areas__r}" var="item">
  <apex:column headerValue="Action">
 <a href="javascript:if (window.confirm('Are you sure? you want to delete - {!item.Location_Area__r.Name} ?')) deleteArea('{!item.Id}');" >Delete </a>
</apex:column>
  <apex:column headerValue="Area">
    <apex:outputLink value="{!URLFOR($Action.Area__c.View, item.Area__c)}">{!item.Area__c.Name}</apex:outputLink>
  </apex:column>

</apex:pageBlockTable>
</apex:output panel >

<apex:actionFunction action="{!deleteArea}" name="deleteArea" reRender="panelId">
 <apex:param name="selectedDelId" value="" assignTo="{!deleteAreaId }" />
</apex:actionFunction>