Having trouble showing and hiding...

I'm creating super simple apps just for practice. The apps allow a user find the areas of certain shapes. The user can select what shape they want to find the area of using radio buttons.

The apps are hidden on page load using this code:

$(document).ready(function(){
        $("#triangle").hide();
        $("#rectangle").hide();
        $("#circle").hide();
});

Here are the radio buttons:

<h2>I need to find the area of a:</h2>
    <form>
        Triangle <input type="radio" name="A" id="triangle_radio"  onClick="showTriangle();" />
    <br>
        Rectangle <input type="radio" name="A" id="rectangle_radio" onClick="showRectangle();" />
    <br>
        Circle <input type="radio" name="A" id="circle_radio" onClick="showCircle();" />
    </form>

When a radio is selected, the corresponding app appears on the page using the function associated with its onClick event:

function showTriangle() {
        $("#triangle").show();
}
function showRectangle(){
        $("#rectangle").show();
}
function showCircle(){
        $("#circle").show();
}

This works pretty well. But if the user clicks on all the radio buttons, all the apps show on the page (even though only one radio is selected at a time). I want the apps to show one at a time. So if the triangle app's radio is selected, it appears. Then, if the rectangle radio is selected, that appears and the triangle app disappears.

I tried to accomplish this with the triangle app. I got rid of its onClick event, and wrote a conditional statement:

if($("#triangle_radio").attr("checked") == "checked") {
    $("#triangle").show();
}

This did not work. Now the triangle app's radio button does nothing.

So how do I make each app appear one at a time, and disappear when its radio is no longer selected?

I hope I explained my problem decently. I'm still quite new to all this, so sometimes I even have trouble explaining it to myself.

I created a CodePen of the entire web page in its current condition: http://codepen.io/sketchcrush/pen/OPmMwe

As you'll see, the rectangle and circle apps appear when their radio is selected. The apps calculate just fine. But the triangle app (the one with the conditional statement) does nothing when you select its radio.

Any help is greatly appreciated.

-Chris A.