Animate rectangle like a stroke

By far the simplest solution is to use a thick stroke on a path with no fill and then just set up Trim Paths. 

If you want a dashed line outline of the shape that can also be easily created using a duplicate layer and the Layer/Auto-trace menu to create a mask that you can copy and paste to a new shape layer as a path, then set up dashes. Here are the Auto-trace settings I used to create this animation in about 2 minutes.*

The Animation:

If you want the dashed lines to animate on you can just use the animated stroke as a Track Matte or as the Source for Set Matte. 

The screenshot shows everything I did to all layers. Trim Paths is a Shape layer animator. You can find more detailed instructions by typing "trim paths" in the Search Help field in the Top Right Corner of After Effects. It is a valuable tool for all users. I use it all the time.

* The "Drag & Drop here..." area is buggy and should not be used to share images. Please use the toolbar or just drag your images to the reply field.

I'm not 100% clear of your goal, but it seems you simply want to animate the object "growing" from a rectangle to a more complex L-shape.

If that's the case, my first suggestion would be to simply create a matte shape with a mask and animate the matte shape.

But, if your object is stroked and filled, and you want those elements to animate, you will need to learn the basics of path animation in order to keyframe the path changes.  typically you would start from the end design's path keyframes, then set keyframes at the point right before the "elbow", then right after the "elbow", then at the start position.  

If you post a more detailed explanation of your goal we can discuss it in more detail.