Circled Square

Since the area of the circumcircle is π，we can get the radius of the circle by using the formula：πr^2=π r^2=1 Apparently r=1 Since it's a square ,each side of it has the ratio √2:1 to half of the diagonal(45˚) Therefore , the area of the square would be √2 *√2 =2. Fairly straightforward. A classic square /circumcircle question.

$\pi r^2 = \pi$ , so $r^2=1$ , and so $r=1$ . If $r=1$ , consider a right-angled triangle with hypotenuse of length $x$ (the side length of the square) and the other two sides of length 1 (the grey lines in the square). $x^2=2$ , so $x=\sqrt{2}$ . The area of the square is $\sqrt{2}^2=\color{#20A900}{\boxed{2}}$ .

As the area of the circumcircle is $\pi$ $\because A=\pi r^2 \Rightarrow r=1$ thus the total area of the square is the sum of two triangles of base $2$ and height $1$ $\therefore A_s=2\times \frac{1}{2}\times 1 \times 2$ $A_s=2$ .

bec the rule of the area of the circle = r ^2 * 3.1415......... and the area of this circle = 3.1415....... so r ^ 2 must be 1 so r = 1 so the diameter = 2 and as you see above the diameter is the diagonal of the square and the hypotenuse of 2 right angled triangles with 45 degrees on both two other sides so by Pythagorean theorem 2^2 = 4/2=2 so the side of the triangle is sqrt(2) so the side length of the square is sqrt(2) so the area of the square is sqrt(2) ^ 2 means 2