I have an iMac (late 2012), as you can see from the photos below the screen is shattered. The LCD panel is undamaged, but the glass is totaled. It is impossible to remove the glass without breaking the LCD panel, as they are merged or something. It is expensive to buy a new screen for these iMacs, and I don't even know if it would be worth the money and effort to repair the display. The machine works flawlessly. If you're wondering how this happened, the iMac fell from my desk and face-planted on the floor. (Running OS X 10.9.5 in case you're wondering)
If it is otherwise working well for you, and if there is an Apple store nearby, I would at least take it in to see what they would charge to fix it.
Late 2012? Repair costing $400-600? Not worth it, in my opinion, unless you absolutely can't afford a replacement. (Check the Apple refurbished store for some discounts on iMacs, too.)
Absolutely worth repair and it is possible to do it yourself following the iFixit tutorial. A replacement LCD will cost around £150 plus the tools required to carry out the repair sold by iFixit. Don't forget the adhesive strips. https://www.ifixit.com/Guide/iMac+Intel+21.5-Inch+EMC+2544+Display+Replacement/15837