Approximately how much of the land area of the British Indian Empire did the Princely States cover?

One-third

British India was divided into two entities: The British Indian Provinces (Punjab, United Province, Assam, etc.) and the Princely States (Hyderabad, Kashmir, Bhopal, etc.).
The British Indian Provinces were directly governed by the British government.
The Princely States were territories ruled by princes and enjoyed a degree of control over their internal affairs until they accepted British supremacy. It was known as the suzerainty or paramountcy of the British crown. The Princely States constituted approximately one-third of the land area of British India.
About one out of four Indians lived under the rule of the Princely States.

Prior to Independence, the British announced that with the end of their rule, the paramountcy of the British crown over the Princely States would also end.
This meant that the Princely States, numbering 565, would become legally independent and could choose to join India, and Pakistan, or remain independent.
The decision of joining India or Pakistan was left to the princely rulers, rather than being determined by the people.