Question 947574
The diameter of the circle is the diagonal of the square, forming an isoceles right triangle with the diameter as hypotenuse and sides of triangle as legs.
So {{{A^2+B^2=C^2}}} and in a square, A and B are equal, and C= diameter:
{{{A^2+A^2=C^2}}}
{{{2A^2=C^2)}}} Divide each side by 2
{{{A^2=(C^2)/2}}} find the square root of each side
{{{A=sqrt((C^2)/2)}}}
{{{A=C/sqrt(2)}}} and since A is the length of the side of the square and C=diameter of the circle:
side of square (S)={{{diameter/sqrt(2)}}}={{{2700m/sqrt(2)}}}
Area of a square=side squared
{{{A=S^2}}}={{{(2700m/(sqrt(2)))^2}}}={{{2700^2/2}}}={{{7290000/2}}}=3645000 sq meters
ANSWER: Area of the square is {{{3.645*10^6m^2}}}