Question

find the area of the square in the figure. the area is (simplify your ar units. square units. x² + y² = 121

Explanation:

Step1: Find the radius of the circle

The equation of the circle is $x^{2}+y^{2}=121$, which is in the standard - form $(x - 0)^{2}+(y - 0)^{2}=r^{2}$. So, $r^{2}=121$ and $r = 11$.

Step2: Relate the radius to the side of the square

The diameter of the circle is the diagonal of the square. The diameter $d = 2r=22$. Let the side of the square be $s$. Using the Pythagorean theorem for the square ($d^{2}=s^{2}+s^{2}=2s^{2}$ since in a square, if the side is $s$ and the diagonal is $d$, $d^{2}=s^{2}+s^{2}$).

Step3: Solve for the side of the square

We know that $d = 22$, so $d^{2}=484$ and $2s^{2}=484$. Then $s^{2}=\frac{484}{2}=242$.

Step4: Find the area of the square

The area of a square $A=s^{2}$. Since $s^{2}=242$, the area of the square is 242 square units.

Answer:

242 square units