Cannot subtract using the pathfinder tool

[Kwisatzh]

I am trying to reduce the backgroiund around my image in Illustrator so that it just forms around the triangle in the image to the right, and therefore doesn't have the "boxy" appearance, rather the purple just shows inside of the box. 

I believe the way to do this is the pathfinder tool, but I am unsure about which one. I've tried "minus back" which would make most sense since the purple is at the back, but this says "please select one or more filled paths".

I have seen advice about using the "expand" tool but that doesn't do anything either. Does anyone have any idea what I might be doing wrong and how I can solve this issue?

I've included the layer tab for convenince.

[SJRiegel]

If the shape below is what you are trying to do, the easiest way would be to draw a new triangle below your other shapes, using a copy of your red shapes as a guide.

  

For this example, I made a the copy, drew connecting lines and made it into a live paint object so I could fill the center. 

Then I expanded the live paint object, and used the shapebuilder to merge it into one seamless shape.

 

[Jacob Bugge]

Kwisatzh,

You can, presuming vector artwork:

1) Copy the Group of red objects and drag it down into Layer 2 so it is on top of the purple background there, and lock the background rectangle, continuing in Layer 2;

2) Delete the red path that is not in a corner;

3) With the Pen Tool Click the corner Anchor Points that point towards the other paths all the way round clicking the first one again; this will form a closed path more or less overlapping the corner paths;

4) Select all Use the Live Paint or the Shape Builder or the Pathfinders (first Divide then Unite);

5) Unlock the purple rectangle, select all and Ctrl/Cmd+7 to create a clipping set, hiding the outer parts of the purple rectangle.