Thanks for the question. The following article provides relevant information for your issue. While it speaks of iPhone, the same steps apply for iPad:
Display does not go into landscape mode
- Remember that photos, webpages, and applications will not change viewing-orientation modes when iPhone is lying flat. Hold iPhone vertically to switch between portrait and landscape modes or vice versa.
- Verify that rotation lock is not on.
- To test, open the Calculator application while holding the iPhone vertically (portrait mode). The standard calculator should appear. Then rotate the iPhone to a horizontal position (landscape mode), and the scientific calculator should appear.
Note: Certain apps and features may support only one mode, landscape or portrait. For example, the Videos app plays video in landscape mode, and Reminders uses only portrait mode. Not all applications on iPhone use landscape mode.
You may also wish to configure the default action of the side switch on your iPad: