Question 986297
TRIANGLE

Find the perimeter, same as the original length of wire.
a, altitude,
x, length of one of the equal sides
Draw the picture.
{{{a^2+(x/2)^2=x^2}}}
algebra steps
{{{a=(sqrt(3)/2)x}}}
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Use the given area
Note that base will be x, height will be a.
We should use the entire triangle 
{{{(1/2)x*a=484sqrt(3)}}}
{{{(1/2)x*(sqrt(3)/2)x=484sqrt(3)}}}
{{{(1/4)x^2=484}}}
{{{x^2=4*484}}}
{{{x=sqrt(4*4*121)}}}
{{{highlight(x=44)}}}
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This means that the <b>perimeter of the equilateral triangle</b> is {{{highlight(132*centimeters)}}}.


SQUARE
Need side length to find its area.  Use known perimeter same as of the triangle.
{{{s*4=132}}}
{{{s=132/4}}}
{{{s=33}}}
AREA of the square, {{{33^2=highlight(1089*cm^2)}}}.


CIRCLE
Need radius to find its area.  Use known perimeter same as of the triangle.
{{{2pi*r=132}}}
{{{r=132/(2pi)}}}
{{{r=66/pi}}}
AREA of the circle is {{{pi*r^2=pi*(66/pi)^2=66^2/pi}}}
{{{highlight((4356/pi)cm^2)}}}
If you want a computed approximation for this you might start with 1386.6.


You might find a ratio of area for Square to Circle any fair way you want.
1089:1386.6 ?Square to Circle
1386.6:1089  ?Circle to Square


If you were to divide BOTH of those numbers composing the ratio by 99, you will get something extremely near to  your expected 14:11.  The circle-to-square ratio.
Other reportable ratios may also work well.