Question 199048
The inscribed square has a diagonal equal to 2 times the radius ( or the diameter) of the circle and this is 2*6 = 12.
If a square has a diagonal of 12, then you can find the length of its sides by using the Pythagorean theorem:
{{{c^2 = a^2+b^2}}} Where c is the diagonal and, for a square, the two sides are equal and a = b, so...
{{{c^2 = a^2+a^2}}}
{{{c^2 = 2a^2}}} Substitute c = 12 (the diameter of the circle).
{{{12^2 = 2a^2}}}
{{{144 = 2a^2}}} Divide both sides by 2.
{{{a^2 = 72}}}
The area of the square with sides equal to a is:
{{{A = a^2}}} Substitute {{{a^2 = 72}}}
{{{highlight(A = 72)}}}sq.units.