It's impossible to speculate without seeing the chances are you are talking about a rotomolded plastic yak. ?
They certainly can be repaired but there is point that its not really doable or worth it. Not only does the size of the damage figure in but where on the kayak. The more that area flexes the more likely it will cause problem again later. If it is very old and cracked due to brittleness there is no point in fixing it.
There are some products for sale to do it yourself.
IT meaning plastic welding. It's not as easy as it sounds. It requires both the repair plastic and the boat be melted and stuck together with heat gun, torh or both. the repair material needs to me more melted than the boat.- you can imagine that could be a little tricky.If the boat is free or little cost you don't have much to lose if things go wrong.
Search plastic kayak repair, supplies and similar. YouTube will have some videos. There are some epoxy type repairs that might work- again depends on the exact damage and kayak overall.
If its worth saving and you can find an outfitter near you that repairs- I'd let them do it.
Www.hardcorekayakfishing.com
Them Hardcore boys