Some theoretical answers were provided, but here's a practical answer from an astronomer's point of view.
(First off, the resolving power is given by diameter, not surface area. So we will talk about diameter here.)
For visible light, the practical resolving power of a 100mm diameter mirror is 1 arcsec. A 200mm mirror: 0.5 arcsec. And so on. This is the rule used by astronomers.
A mirror "with 20x the surface area of the Sun" (apparent area, I assume) would have approx 4.5x the diameter of the Sun, which is 6.3 x 10^6 km. Such a mirror would have a resolving power of 1.6 x 10^-11 arcsec.
At 10 light years distance, such a mirror would resolve details as small as 7 meters.
Please note this discussion is entirely theoretical, as there are no known technologies to manufacture such a big mirror with the required precision for visible light astronomy optics - which means the surface error cannot be bigger than 100 nanometers - in fact, for a good mirror, the acceptable error is 4x ... 5x smaller. There's no way to maintain such precision across millions of kilometers of reflective surface.
Currently, the biggest monolithic mirror is 6m in diameter and it never performed very well. The biggest well-performing monolith mirror is 5m. The biggest segmented mirrors are 10m in diameter, with a 40m project having had its initial funding approved very recently.
There are lots of mathematical answers to this question, but I'd like to make a few qualitative observations instead, based on 54 years using telescopes of all kinds and sizes, from 40mm refractors to 74-inch reflectors.
- Unless you have some specialized purpose, don't consider anything
smaller than 6 inches aperture. Small telescopes look cute, but don't
show you much, especially if you're a beginner. Experienced observers
can tease amazing observations out of tiny scopes, but most of us
will be happier to give these a pass. Aperture wins.
- A 10-inch Newtonian on a Dobsonian mount is something of a "sweet
spot." It's about the smallest aperture to show significant detail in
deep sky objects, yet is compact and light enough to be easily
transported to dark sky sites.
- Above 10-inches, the more aperture the better, provided you can
comfortably transport, set up, and operate it. This is crucial! The
nicest telescope in the world is useless if it never gets used. I
find even a 12-inch Dob becomes bulky, cumbersome, and heavy.
Aperture wins, but only if you use it.
Best Answer
Telescope resolution is all about apparent angles. From the sounds of it, the lowest resolution you'd settle for would be something capable of resolving about $1 \operatorname{cm}$ objects, right? Well, the distance between the Earth and Mars varies, depending on the time of year, from around $0.5\operatorname{AU}$ to $2.5\operatorname{AU}$ ($7.5\times 10^{10} \operatorname{m}$ to $3.7\times 10^{11} \operatorname{m}$). At those distances, a $1$ centimeter object subtends an angle of $$\theta = \frac{s}{d},$$ which is $1.5\times 10^{-13}\operatorname{rad}$ to $2.7\times 10^{-14}\operatorname{rad}$.
The resolution of a circular telescope is given by the formula $$\theta = \frac{1.22\lambda}{D}.$$ So, assuming you're using visible light, with $\lambda \approx 500\operatorname{nm}$, to resolve those $1$ centimeter objects it would require telescopes with a diameter of $D=4.6\times 10^6\operatorname{m}$ to $7.4\times 10^7\operatorname{m}$. For reference, the diameter of Earth is about $1.3\times 10^7\operatorname{m}$.
Note that the sheer size is only one of the challenges. In order to achieve this theoretical resolution you would need the surface of the mirror to have the correct shape everywhere to within about a wavelength of light. In other words, this Earth-sized mirror could not have any imperfections larger than about $500\operatorname{nm}$. To see some of the information related to getting ordinary lenses and mirrors correct to this level see the Wikipedia article on optically flat.