   # Area of a circle using the circumference

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You have a patch of dead shrubs you want replaced with sod. But there's a hornet's nest in the middle, and therefore to avoid
getting stung you can't measure the radius or diameter to plug into the formula: area = pi r squared.

And in order to get a price quote from the landscaper you need the square footage.

You can however easily measure the circumference.

Question: what is the area of this circle of dead shrubs if the circumference is 100 ft? posted Sep 14, 2016

+1 vote

circumference of circle = 2*Pi*R = 100ft
or R = 50/Pi

Area = Pi * R * R
=> Pi * 50 *50 / (Pi * Pi)
=> 2500/Pi
=> 796.17 Ft2 (Pi = 3.14) answer Sep 14, 2016
There is a 1 step formula you can use if you know only the circumference:
Area = C^2/12.56 = 10,000/12.56 = 796.17 sq ft. (same as yours)
I derived it using simple substitutions and cancellations which resulted in -
circumference sq/4 pi.

And since 4 pi is a constant, you can check on your landscaper's price quote
with just one quick mental calculation.

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