What is the cause of prolonged tiredness? even after a good nights sleep. i wake up fine but by 11. i am drained

Sleep comes in various stages & with deep sleep being the most effective in restoring vigor. If your "time" asleep is pretty normal but you are not restored, it suggests you are not entering deep sleep stages. I would visit your doc with this in mind. An exam may reveal some issues or a sleep study may help identify it. Sleep disturbances are one of the most under diagnosed problems in health.

To fully understand etiology, you will likely need to undergo overnight sleep study. A sleep disorder such as narcolepsy, could be considered, but thyroid problems, anemia, might explain this. Your physician can do testing and arrive at answers.

It is not feasible to provide a meaningful opinion without taking additional history, physical examination and may be some tests. It would be prudent to see your doctor and discuss if you may be depressed. Counter-intuitive as it may seem, exercise may help. Start with low intensity exercise such as walking and gradually increase the intensity as tolerated. Drink more water. Wish you good health!

If you feel drained but not sleepy during the daytime, it is less likely you lack of sleep because of sleep apnea but you may have a health problem, either physically or mentally. You need to see a doctor for a complete check-up.