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32 feet of fencing....determine the maximum area that can be enclosed with the fencing to make a flower garden?

You have 32 feet of fencing and want to determine the maximum area that can be enclosed with the fencing to make a flower garden. You do not want to deal with fractions or decimals, so you are limiting the dimensions to whole numbers. If the garden were circular in shape, what area could be enclosed with the 32 feet of fencing?

Public Comments

1. Go with the perfect circle. The circumference of your circular fence would be 32 feet, so the radius would be 32 / (2 * pi), or 16/pi. So the area would be pi * (16/pi)^2 = 256 / pi.
2. If there are 32 feet of fencing and the garden's shape is a circle then, the circumference C = 32 = 2(pi)r where r = 16/pi = 5.09 ft and since a whole number dimension is specified, then the radius of the circular garden is 5 ft. And with this dimension, the area of circular garden is A = pi(r^2) = 25(pi) sq ft. Hope this helps.