As has been stated TWICE, the iPad 3 IS NOT compatible nor eligible for installing iOS 10.
The iPad 2, 3 and 1st generation iPad Mini are all ineligible and excluded from upgrading to iOS 10.
They all share similar hardware architectures and a less powerful 1.0 Ghz CPU that Apple has deemed insufficiently powerful enough to even run the basic, barebones features of iOS 10.
Why would you want to upgrade, anyways?
Since iOS 8, older iPad models such as the iPad 2, 3 and 4 have only been getting the most basic of iOS features.
Older iPad users get none of the newest and coolest cutting edge features that newer model iDevices, with better hardware specs, can handle with more aplomb.
Plus, these are the only two supported models left that use the much outdated 30 pin dock connector.
FYI,
Just because your iPad 3 is no longer able to upgrade to the latest iOS doesn't mean youriPad 3 is suddenly useless.
Your iPad 3 will work as it always has and the apps you have installed on it will continue to update and receive some level of app updates relevent to your current iOS.
You have had four years of iOS upgrades and updates.
Your iPad 3 will still do everything it does now and you will, get, at least, another full year, perhaps two, if you decide to you want to wait longer to get a new or newer iPad model.
I just needed to put that out there for you.
Your iPad 3 is NOT suddenly becoming obsolete.
Good Luck to you!