Answer: Grass probably won't grow in the spot due to the shade cast by the trees but groundcover will grow there. The bonus is that you won't have to mow! To facilitate drainage you may have to install a curtain drain (or French drain) by digging 2' deep trenches along the perimeter of the site, dumping in some gravel, laying a perforated pipe, covering it with more gravel and then the soil you removed from the hole to bring the area up to the right level. The pipes will collect and divert the water and the site should drain faster for you. Hope this helps!
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