re: Best grass to have in a shaded area

The cold, hard truth here is you are going to have issues with any grass type with that little sunlight a day. You can make it work by sodding and then replacing it every few years. Once you sod though, it's going to start thinning out if it doesn't get enough sunlight.

I would personally look into a shade-tolerant zoysia like Geo Zoysia. There are several different varieties that are better in shade than others.