Got marked wrong because I didn't write "the thirteenth page of the book" - but Duo has accepted this sort of answer with the initial determiner missing before.
I got marked wrong for writing "thirteenth" but then the system accepted "thirteen". I reported this.
I would not have particularly resented being faulted for writing 'Page 13 of the book' – after all this lesson is largely about ordinal numbers, and if I lazily take a short cut I must accept the consequences – but the person who stipulated 'The 13 page of the book' as the only correct answer has no business to be telling me or anybody else what is right or wrong in English usage!
Is "тринадцатая страница" is a pretty common way of saying what in English would often be just "page 13"? I recall seeing Russian chapters labeled with ordinal numbers (which would be very uncommon in English) and wonder if the same applies for pages.
Both ways are common. The difference is that "тринадцатая страница" sounds more relaxed and therefore is more often heard in speech (including in class when the teacher asks the students to open a certain page of their books) while "страница тринадцать" is colder and more formal, so it is more often seen in writing, e.g. academic/scientific works. The latter also is what the abbreviations "стр.13" or "с.13" stand for:
См.с.13 = Смотри страницу 13 = See page 13.
"книга в тринадцать страниц", but we usually use "there are thirteen pages in the book" - в книге тринадцать страниц.