The first requirement is to read your declarations to determine what duty belongs to whom. I assume that the St. Augustine (grass?) is the front lawn and it is escaping care. You may find that the short-run solution is to do it yourself while you bug the HOA to do its duties, including lawn maintenance. Does the HOA have enough money in the till to pay for these responsibilities, or is there a money shortage.
Finally, talk to a lawyer about what specific relief is available under the documents and the statutory law.
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I'm not sure how you equate your side yard to common grounds. Normally, you yard is your responsibility and is not common grounds. There are a few HOAs out there that do take care of the owners' yards and it is included in the assessments, but if your documents do not specifically state the HOA will take care of your property, then their duty to maintain common grounds does not include your yard. This is assuming you live in a HOA (single family homes) and not a COA (condominium association).
There was a revision to the laws in 2009 which prohibits associations from enforcing landscaping restrictions that would interfere with the owners right to have Florida Friendly Landscaping. The concept is to cut down on watering, herbicides, pesticides and other practices which do not conserve Florida's natural resources. This includes requiring specific sods, such as St. Augustine grass, if the lot cannot accommodate the specific sod without excessive use of resources such as watering. I am sure the law would be reciprocal to allow the HOA to choose a different sod for common areas.
If the common areas are not being maintained at all, then that is a question worth investigating. If your HOA is running low on funds for maintenance they will need to increase assessments to pay for it. HOAs generally do not have any resources for income other than the assessments the owners pay so any increase in expenses has to be the burden of the homeowners.
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