The area of a circle is 220 sq. cm. The area of a square inscribed in this circle will be

### Concept & Inscribed Square For a square inscribed inside a circle, the diagonal of the square is equal to the diameter of the circle ($2r$). The area of a square can be found directly from its diagonal $d$. $$Area\ of\ Square = \frac{d^2}{2} = \frac{(2r)^2}{2} = 2r^2$$ ### Step-by-Step Solution * Given Area of the circle $= 220$ cm². * Formula for circle area: $\pi r^2 = 220$. * Solve for $r^2$: $\frac{22}{7} \times r^2 = 220$ $r^2 = \frac{220 \times 7}{22} = 10 \times 7 = 70$. * The diagonal ($d$) of the inscribed square equals the diameter of the circle ($2r$). * Area of the square $= \frac{1}{2} \times d^2 = \frac{1}{2} \times (2r)^2 = \frac{1}{2} \times 4r^2 = 2r^2$. * Substitute the value of $r^2$ into the area formula: $Area = 2 \times 70 = 140$ cm². ### Exam Strategy & Shortcut Memorize the direct relationship: Area of Inscribed Square $= \frac{2}{\pi} \times Area\ of\ Circle$. Using $\pi = \frac{22}{7}$, Area of Square $= Area\ of\ Circle \times \frac{7}{11}$. Therefore, $220 \times \frac{7}{11} = 20 \times 7 = 140$ cm². This skips solving for $r$ entirely. ### Common Pitfall A common mistake is finding $r^2=70$ and then trying to take the square root to find $r$, which leads to messy decimals. Always look at what the final formula requires; here it needs $r^2$, so leave it as $70$. ### Final Answer Therefore, the correct answer is **140 cm²**.