What is the circumference of 12.56 square meters?

Answer 1

it doesn't matter what the shape of the area is, because it's all the same measurement, so we can assume it's a circle. the formula for the area of a circle is πr2. lets solve for r.

πr2=12.56

r2=12.56/π

12.56/π is roughly the same as 4 (if pi is 3.14, it is exactly the same, so it probably found using pi as 3.14)

r2=4

r= √4

r=2

we now have the radius of a circle, to find the circumference, we use the formula pi*diameter and diameter is the same as radius*2.

r*2=d

2*2=d

d=4

π*d=circumference

π*4

we will assume pi is 3.14 because we assumed the area was found using pi as 3.14

(3.14)*4

12.56

the answer is roughly 6.28. but what if we need a more exact answer, lets solve it again, but lets get an equation instead of a number.

πr2=12.56

r2=12.56/π

r= √(12.56/π)

r*2=d

√(12.56/ π )*2=d

π*d=circumference

π*( √ (12.56/π)*2 )

2π*√ (12.56/π)

now we got a perfect answer. if we need a number, just replace pi with a number as close to pi as you want and solve. this equation works, but we can simplify it even more if we want to.

√4π2*√ (12.56/π)

√(4π2*12.56/π)

√(4π*12.56)

√(50.24*π)

lets test it to make sure it works. if we plug in 3.14 into pi and solve, we should get the same answer as before. (25.12)

√(50.24*(3.14))

√(157.7536)

12.56

our equation works! now lets make an equation out of it that helps us solve all problems like this. 12.56 will be replaced with A.

πr2=A

r2=A/π

r= √(A/π)

r*2=d

√(A/ π )*2=d

π*d=circumference

π*( √(A/π)*2 )

2π*√(A/π)

we got an answer, but we still can simplify.

√4π2*√(A/π)

√(4π2*A/π)

√(4π*A)

√(4Aπ)

we have a equation to convert from area to circumference. lets make sure it works. if we plug in 12.56 for A and 3.14 for pi, we should get 12.56

√(4(12.56)(3.14))

√(156.7536)

12.56

it works. just to wrap things up, the rough answer with 3.14 as pi is 12.56. an exact answer with pi left as pi is √(50.24*π). the formula to find an answer to any similar problem is √(4Aπ).