Your iPad screen must be replaced. As is, the screen is a safety hazard (as you have demonstrated) - added to which the screen digitiser (that responds to touch) will at best be severely compromised.
You can check availability/eligibility for repair - and associated cost for your country/region - here:
iPad Repair & Service - Apple Support
In addition to Apple's mail-in repair service, you can arrange repair at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP):
Genius Bar Reservation and Apple Support Options - Apple
For practical purposes, in lieu of repairing and returning your own iPad, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for repair. Unless you have benefit of an active AppleCare plan, an out-of-warranty repair while expensive will be somewhat less than the cost of a replacement iPad.