Question Number 28202 by naka3546 last updated on 21/Jan/18
Commented by naka3546 last updated on 21/Jan/18
$${If}\:\:{area}\:{the}\:{smallest}\:{square}\:{is}\:\mathrm{1}\:{cm}^{\mathrm{2}} \:. \\ $$$${find}\:{the}\:{area}\:{of}\:{red}\:{region}\:.\: \\ $$$$ \\ $$
Answered by mrW2 last updated on 22/Jan/18
Commented by mrW2 last updated on 22/Jan/18
$${red}\:{area}=\left(\frac{\pi\mathrm{3}^{\mathrm{2}} }{\mathrm{4}}−\frac{\mathrm{3}×\mathrm{3}}{\mathrm{2}}\right)−\left(\frac{\pi\mathrm{1}^{\mathrm{2}} }{\mathrm{4}}−\frac{\mathrm{1}×\mathrm{1}}{\mathrm{2}}\right) \\ $$$$=\frac{\mathrm{9}\pi}{\mathrm{4}}−\frac{\mathrm{9}}{\mathrm{2}}−\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$=\mathrm{2}\left(\pi−\mathrm{2}\right) \\ $$$$\approx\mathrm{2}.\mathrm{28} \\ $$