the rule basically states that any point on the ceiling should be within times the listed spacing of a detector. if we take a typical 30×30 listed spacing, that means any point on the smooth ceiling should be within 21ft of a detector. so in your example start drawing circles with a radius of 21ft and put the detector in the center of the circle make sure that your circles cover the entire octagon. I would say 4 detectors should cover the area. also bear in mind that this is for ceilings 10ft and lower. if ceiling is greater than 10 feet, than you have to adjust the spacing.
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