Question 1119330
A_square = {{{s^2}}}

A_circle = {{{pi*r^2 = pi*(s/2)^2 = pi*s^2/4 }}}

{{{pi/4 }}} is 0.7854 to 4 decimal places

So A_circle = A_ square*0.7854

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Dear Student:

 {{{pi }}} is divided by 4 when one tries to express the area of the circle <em>in terms of the area of the square</em>:

    A_circle = {{{ pi*r^2 }}} —> = {{{ pi*(s/2)^2 }}}  <<< this is A_circle in terms of the sides of the square (s). You must divide the side of the square by 2 to get the radius of the circle.  After squaring, it becomes 4 in the denominator.<br>

Continuing…   = {{{ pi*(s^2/4) = (pi/4)*s^2 }}} = approx 0.7854*{{{s^2}}} = 0.7854*A_square.


I hope you see it now.   

Note that you must somehow know the area of the square (or equivalently, the side length of the square so you can calculate the area) in order to use this formula to find the area of the circle, it simply relates the two areas.