Question Number 98560 by I want to learn more last updated on 14/Jun/20
Commented by I want to learn more last updated on 14/Jun/20
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area}. \\ $$
Answered by HamraboyevFarruxjon last updated on 14/Jun/20
$$\boldsymbol{{S}}\left(\boldsymbol{{romb}}\right)=\boldsymbol{{a}}^{\mathrm{2}} ×\boldsymbol{{sin}\alpha}=\mathrm{81}×\boldsymbol{{sin}}\mathrm{70}° \\ $$$$\boldsymbol{{S}}\left(\boldsymbol{{sector}}\right)=\frac{\mathrm{70}°}{\mathrm{360}°}×\boldsymbol{\pi}×\mathrm{9}^{\mathrm{2}} =\frac{\mathrm{63}\boldsymbol{\pi}}{\mathrm{4}} \\ $$$$\boldsymbol{{S}}\left(\boldsymbol{{shaded}}\right)=\boldsymbol{{S}}\left(\boldsymbol{{romb}}\right)−\boldsymbol{{S}}\left(\boldsymbol{{sector}}\right)= \\ $$$$=\mathrm{81}\boldsymbol{{sin}}\mathrm{70}°−\frac{\mathrm{63}\boldsymbol{\pi}}{\mathrm{4}}\approx\mathrm{26},\mathrm{63} \\ $$
Answered by mr W last updated on 14/Jun/20
$${r}=\mathrm{9}\:{cm} \\ $$$$\theta=\mathrm{70}°=\frac{\mathrm{7}\pi}{\mathrm{18}} \\ $$$${A}_{{shaded}} ={r}^{\mathrm{2}} \left(\mathrm{sin}\:\theta−\frac{\theta}{\mathrm{2}}\right)=\mathrm{9}^{\mathrm{2}} \left(\mathrm{sin}\:\frac{\mathrm{7}\pi}{\mathrm{18}}−\frac{\mathrm{7}\pi}{\mathrm{36}}\right) \\ $$$$=\mathrm{26}.\mathrm{636}\:{cm}^{\mathrm{2}} \\ $$