How is the best form to obtain an square with the same area os a circle?

Answer 1

There is no way to do it exactly; this is one of the famous problems of antiquity which was eventually proven impossible to solve. So the best bet is to do it numerically; given the area of the circle (measure it if necessary), the side of the square will simply be the square root.

Answer 2

The area of a circle is pi * the square of the circle's radius. The irony of this is that pi itself is calculated, in theory, by trying to approximate a circle with a square (or really, an increasingly large amount of smaller and smaller squares).

The area of a square is simply the square (hence the term) of one side. Since you want the area of your square to be the same as the area of your circle, you can find the length of one side of the square by taking the square root of the area of the circle. This will simply be the radius of the circle times the square root of pi (approx 1.77).

So it ultimately depends on what information you are given. If you are given the area of the circle, simply take the square root and use that as the length of one side. If you are given only the radius, multiply that by the square root of pi to get the length of one side.

Answer 3

To draw a square having the same area of a circle,first of all you have to know "r" the radius of the circle
Now draw a rectangle having one side equal to 3.14*r and the other side eqal to r.You may draw a rectangle with one of the sides equal to 1.57 r and the other side 2r.
Let ABCD be the rectangle.
Produce DC and from DC produced the portion of CE is cut off making equal to CB.
A semi-circle is drawn on DE,the centre of which can easily found out by bisecting DE.
BC is produced to meet the semi-circle at F
Now draw square CFGH with each side equal to CF
Square CFGH will have the same area as that of a circle with radius r
Please note that in the above explanation I have followed AB as the base of the rectangle and is equal to 3.14r and AD and BC are the vertical sides of the rectangle equal to r.

Answer 4

1) The area of any circle, Acircle = PI * R^2; where R is the radius of the circle.

2) The area of any square, Asquare = S^2; where S is the lenght of every side.

3) Acircle = Asquare when S^2 = PI * R^2

4) The area of a circle, of radius R, equals the area of a square of side S, if, (S / R)^2 = PI

Answer 5

There's only one way to do it:
1) Found the ares of the circle = 3.14 x r^2
2) Found the square root from the circle area (3.14 x r^2)^1/2
That will be the size from each side of your square.
Area from a square = side^2
Then, as (n^1/2)^2 = n
[(3,14 x r^2)^1/2]^2 = 3,14 x r^2 = area from the circle.

Answer 6

Compute the square root of the circle's area.
The result is the square's side length.

Answer 7

This is where the phrase "Squaring the Circle" comes from.

It's an ancient problem that is impossible in the sense the ancients meant it because pi is irrational.

Answer 8

r1 = (1/2)x
x = 2r1
As = 4(r1)^2

Ac = pi * (r2)^2

4(r1)^2 = pi * (r2)^2
((r1)^2)/((r2)^2) = pi/4
(r1/r2)^2 = (pi/4)
r1/r2 = (1/2)sqrt(pi)

or you can say

r1 = ((r2)/2)sqrt(pi)
or
r2 = (2r1 * sqrt(pi))/pi

to make it simplier, you can write it like this

y = (xsqrt(pi))/2
or
x = (2ysqrt(pi))/pi

whereas r1 is the radius of the square and r2 is the radius of the circle.