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Question Number 127740 by Algoritm last updated on 01/Jan/21

Commented by Algoritm last updated on 01/Jan/21

$$\mathrm{yellow}\mathrm{shaded}\mathrm{area}=?$$

Commented by mr W last updated on 02/Jan/21

$$doyouhavethecorrectanswer?$$$$igotshadedarea=\frac{areaofsquare}{24}.$$

Commented by mr W last updated on 02/Jan/21

$$why{don}^{\prime }tyouanswerthissimple$$$$questionfromme?$$

Commented by Algoritm last updated on 02/Jan/21

$$\mathrm{yes}\mathrm{sir}$$

Commented by mr W last updated on 02/Jan/21

$$thankyousir!$$

Answered by mr W last updated on 01/Jan/21

Commented by mr W last updated on 01/Jan/21

$$\tan \alpha =\frac{1}{2}$$$$\tan 2\alpha =\frac{2\times \frac{1}{2}}{1-{\left(\frac{1}{2}\right)}^2}=\frac{4}{3}$$$$\beta =\pi -2\times 2\alpha =\pi -4\alpha$$$$\sin \beta =\sin 4\alpha =\frac{2\times \frac{4}{3}}{1+{\left(\frac{4}{3}\right)}^2}=\frac{24}{25}$$$$shadedarea={\left(\frac{a}{4}\times \sin 2\alpha \right)}^2\times \frac{1}{\sin \beta }$$$$=\frac{a^2}{16}\times {\left(\frac{4}{5}\right)}^2\times \frac{25}{24}=\frac{a^2}{24}$$

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