Required percentage of vegetated area.

The language from the LEED v4.1 reference guide states: "Provide outdoor space greater than or equal to 30% of the total site area (including building footprint). 25% of the minimum 30% total outdoor space requirement must be planted with a diversity of vegetation or have overhead vegetated canopy." So in simple math if your site area including building footprint is 100,000 sf you need at least 30,000 sf of open space meeting the LEED definition, at least 7,500 sf of that open space needs to be vegetated per the LEED definition. 

The problem you're having is that your dedicated open space is actually bigger than basic requirements and that's also skewing the amount of vegetated areas you need. You're correct that at a high/basic-level, you need 7.5% of your total site area to have the correct vegetation. That 7.5% number, however, only works if you have exactly 30% of your total site area as dedicated open space. When you increase the amount of dedicated open space you have, your minimum vegetated area also increases - because you need 25% of whatever land you dedicate to be permanent open space. Using the 100,000 sf values Summer had and the percentages you listed, with 55% (55,000 sf) being dedicated open space, you need at least 13,750 sf to be vegetated (25% of that dedicated 55,000 sf). Because your dedicated open space is so much higher than the minimum 30% required, your vegetated area is also higher (13.75% of total).

You have a couple of options to earn the credit: 

1) Increase the vegetated area, if possible, up to that 25% level of your dedicated permanent open space.

2) Decrease the amount of area you dedicate as permanent open space down to closer to the 30% level/whatever works for your actual vegetated area. This doesn't necessarily require a physical change,  but would need a plan highlighting which spaces are permanent/will be maintained and which spaces are not dedicated/could be built-over or developed in the future.