How can I pass a parameter to a function without it running right away?

Have showArea return a function that works with the id.

function showArea(id) {
   return function() {
       // do stuff with id
   };
}

The returned function closes over id so it continues to reference it, and is passed to addListener to be used as the handler.

---

Alternately, you could just inline the function that calls showArea(1)…

google.maps.event.addListener(southEast, 'click', function() { showArea(1); });
function showArea(id) {
   // do stuff based on that id
}

This will work because you’re hardcoding the 1. If it was a variable that could change, like in a loop, you’d use the first example.