Answer: If the shade is very dense, grass will have a hard time getting established and staying healthy, especially with heavy traffic. The most shade-tolerant grasses are fine fescues, but they are moderately tolerant of wear. A tall fescue variety is probably the best compromise, though they are not as shade tolerant. For best results, choose a variety that is known to grow well in your area. A lawn professional can help you. Test the soil and amend as recommended; and once you've seeded the area, make sure it's protected from all traffic until the grass is growing well. Since trees and grass will compete for moisture, make sure there's plenty available while the grass is getting going, and then gradually wean the lawn off irrigation. Mow the shaded area higher than sunny areas -- the grass needs more leaf surface to catch as much light as possible. Use about 10% less fertilier on the shaded area than you do on your sunny spaces.
Another alternative is to landscape the area differently: put in raised beds, a patio or paths, and grow shade-tolerant groundcovers instead. Hope this helps!
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