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Annette wants to plant flowers around her new patio which, as shown below, is comprised of a hexagon and a connected square. She intends to plant the flowers $6\text { inches}$ apart on all the edges of the patio except the one side of the square which is the entrance to the patio.

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If each of the patio's sides has the length of $5\text{ feet}$ and she plants her first flower at the entrance corner, what is the greatest number of flowers she needs to purchase?











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