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Question Number 199854 by sonukgindia last updated on 10/Nov/23

Answered by aleks041103 last updated on 10/Nov/23

$$everyfoldisdoneattheanglebisector$$$$\Rightarrow finalaccuteangle=90°/4=22.5°$$$$S=8\times 6-2\times \frac{3\times \left(\frac{3}{tan(22.5°)}\right)}{2}=$$$$=48-9cot\left(\frac{45°}{2}\right)=48-9cot\left(x\right)=48-9z$$$$$$$$cot\left(2x\right)=\frac{{cot}^{2}x-1}{2cot\left(x\right)}$$$$$$$$cot\left(45°\right)=1=\frac{{cot}^{2}x-1}{2cot\left(x\right)}=\frac{z^2-1}{2z}$$$$\Rightarrow z^2-2z-1=0$$$${(z-1)}^2-2=0\Rightarrow z=1\pm \sqrt{2}$$$$cot\left(45°/2\right)>cot\left(45°\right)=1\Rightarrow z=1+\sqrt{2}$$$$\Rightarrow S=48-9(1+\sqrt{2})$$$$S=39-9\sqrt{2}$$

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