My iPad is brand new and the back of it is extremely hot

It is not unusual for an iPad to become warm when being used or being charged - more so when using some types of iPad case. High screen brightness and/or CPU intensive Apps will also create more heat - and shorten the time between battery charges.

The key point is that whilst your iPad may become very warm in normal use, the iPad should not become uncomfortably hot to handle. If your iPad is becoming too hot to hold, or if you are concerned that the iPad is not performing as it should, you would be best advised to take your iPad along to the Genius Bar at your local Apple Store - where the technicians can examine and test your iPad for faults.

Genius Bar Reservation and Apple Support Options - Apple

As for battery autonomy, consider that Apple’s quoted runtime for iPad is an “up to” figure. This figure will have been established on the basis of average usage - for tasks that are not particularly CPU intensive, with screen brightness typically 40-50% of maximum. If you are using your iPad outdoors, or in very bright ambient lighting conditions, your screen brightness will be operating at (or close to) maximum.

High screen brightness will significantly reduce the maximum time that the iPad can run on its battery alone before it must be recharged.

A brand new Apple device has many chores to perform to get properly set up.

Once you have allowed some time for the chores to complete, if the heat persists, read and follow the article linked above.