How has the total area of continents changed during the Earth history?

Question

Earth's total land area has increased throughout its history according to this video. What is the dependence of the total area of continents from time?

Answer 1

I think the question is asking about the trend, i.e., how did we get from zero continental crust to about 30 % over the Earth's history? Was it linear, another trend? Well, one figure is enough to show that we don't know:

Selected crustal growth models, from Hawkesworth et al. (2019)

Some think all continental crust formed early in Earth history, and nothing since then, others think it was more progressive, proposing very different trends...

One classical way to infer crustal growth is by dating zircons, a very resistant mineral that is used to infer the presence of rocks that are themselves long gone. It's been known for a while that zircons present some age peaks across Earth's history, but their are some disagreements on the interpretation. From Condie et al. (2017):

There is an ongoing debate about the interpretation of zircon age peaks in igneous rocks and detrital sediments (Rino et al., 2004; Arndt and Davaille, 2013; Hawkesworth et al., 2013). The conventional interpretation is that the age peaks correspond to peaks in production of new continental crust extracted from the mantle (Stein and Hofmann, 1994; Condie, 1998; Albarède, 1998). However, this interpretation has been challenged by advocates of recycling and preservation models; they propose that the peaks record periods of enhanced preservation of crust during the assembly of supercontinents (Condie and Aster, 2009, 2010; Hawkesworth et al., 2010; Voice et al., 2011).

In summary, it is a hot research topic which is still very much debated. If someone has the answer here at Stack Exchange, he/she should apply for the Penrose medal! :)

Answer 2

It is widely thought that when the Earth first formed there was no continental crust. Subduction is largely responsible for the creation of continental crust. If true, and there is no reason to think this is not true, continental crust has grown from nearly zero percent of the planet over three billion or so years ago to covering about 30% of the planet today.

Continental crust is subject to erosion. As ever more continental crust formed, progressively more of it eroded and washed to sea. Most geologists think the formation of new crust and degradation of old crust have long been in balance.