Question 328750
{{{drawing(300,300,-10,10,-10,10,line(6,6,6,-6),line(6,-6,-6,-6),line(-6,-6,-6,6),line(-6,6,6,6),blue(line(0,0,6,0)),locate(2,4,12),locate(3.5,0,a),locate(6.5,3,a),circle(0,0,.3),green(line(0,0,6,6)),circle(0,0,6sqrt(2)))}}}
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From the diagram,
{{{a^2+a^2=12^2}}}
{{{2a^2=12}}}
{{{a^2=6}}}
The side of the square is {{{2a}}}.
The area of the square is then,
{{{A=4a^2}}}
{{{A=4(6)}}}
{{{highlight(A=24)}}}sq. mm.