SOLUTION: 20 ft. is diameter of a circular pond. Determine side of a square pond with equal area.
Area of circle = pi * r^2
Area of square = s^2
3.1416 * 10 = 31.416 sq. ft.
N
Area of circle
A = pi*r^2
A = pi*10^2
A = pi*10*10
A = pi*100
A = 100pi ... exact area in terms of pi
A = 100*3.14
A = 314 .... approximate area of the circular pond
Set this equal to s^2 and solve for s
s^2 = 314
s = sqrt(314)
s = 17.7200451466693
The square pond would have a side length of roughtly 17.72 feet if we wanted the same area as the circular pond.
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Keep in mind that pi = 3.14 is an approximation, and technically not a very good one at that. To get more accuracy, you would use more decimal digits in pi
If you were to use say
pi = 3.1415926535898
then,
A = 100pi
A = 100*3.1415926535898
A = 314.15926535898
is the area of the circular pond
and,
s^2 = 314.15926535898
s = sqrt(314.15926535898)
s = 17.7245385090551
So we still get 17.72 roughly, though the digits afterward are different from before. It all depends on the level of accuracy you require.
Many textbooks and teachers though use pi = 3.14 just to keep things fairly simple. So it might be best to ask the teacher which they prefer.