Question 258711
In this problem, the diagonal of the inscribed square is the same as (equal to) the diameter of the circle.
The diagonal (D) of the square is:
{{{D = sqrt(4^2+4^2)}}} from the Pythagorean theorem.
{{{D = sqrt(32)}}}
{{{D = 4*sqrt(2)}}}
Now that you have the diameter of the circle, you can find its circumference (C) from:
{{{C = (pi)D}}} Substitute {{{D = 4*sqrt(2)}}}
{{{C = (pi)*4*sqrt(2)}}} or...
{{{highlight(C = 4(pi)sqrt(2))}}}
The area (A) of the circle is:
{{{A = (pi)(D/2)^2}}}
{{{A = (pi)(4*sqrt(2)/2)^2}}} Evaluate.
{{{A = (pi)(16*2/4)}}}
{{{A = (pi)*8}}} or...
{{{highlight(A = 8(pi))}}}