The perimeter of a hexagon with an apothem of 12 is 83.14
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No, that is not correct.
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Area of circle = 225 cm2 implies radius = 8.46 cm (approx) Therefore, apothem of hexagon = 8.46 cm then side of hexagon = apothem*2/sqrt(3) = 9.77 cm (approx) and so perimeter = 6*side = 58.63 cm
The area of a hexagon with a perimeter of 12 units is about 10.4 units2
If it is a regular 6 sided hexagon then its perimeter is 6 times 12 = 72 inches