Question

If the area of a square inscribed in a semicircle is $2{cm}^2$, then the area of the square inscribed in a full circle of the same radius is

• A. $5{cm}^2$
• B. $10{cm}^2$
• C. $5\sqrt{2}{cm}^2$
• D. $25{cm}^2$

Answer 1

The correct option is A $5{cm}^2$

$r=\sqrt{{\left(\sqrt{2}\right)}^2+{\left(\frac{\sqrt{2}}{2}\right)}^2}=\sqrt{2+\frac{1}{2}}=\sqrt{\frac{5}{2}}$
$2r=\sqrt{2}b\Rightarrow b^2=2r^2=2{\left(\frac{\sqrt{5}}{2}\right)}^2=5$