13'x13' = 169 square feet
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You will need approximately 23.4 tiles, so 24 tiles. Assuming 13x13 tiles is in inches.
Each tile will be one square foot. So you have 135 square feet.
About 197 (196.875) 16" x 16" tiles will feet in that area.
Each tile will cover 2 square feet. So you will need 12.5 tiles.
It takes 4 6x6 inch tiles to cover a square foot. You will need 180 tiles, plus some for spoilage and mistakes.