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Question Number 193880 by Mingma last updated on 22/Jun/23

Answered by Subhi last updated on 22/Jun/23

$$putlengthofeachside=l$$$$BAF=120\Rrightarrow AFB=ABF=\frac{180-120}{2}=30$$$$\frac{BF}{sin\left(120\right)}=\frac{l}{sin\left(30\right)}\Rrightarrow BF=\sqrt{3}l$$$$\frac{1}{2}{l}^2.sin\left(120\right)=2\Rrightarrow l=\sqrt{\frac{8\sqrt{3}}{3}}$$$$BF=3.7224\Rrightarrow BG=1.7224$$$$EG=\sqrt{\frac{8\sqrt{3}}{3}+2^2}=2.936$$$$IG=\sqrt{{(\sqrt{\frac{8\sqrt{3}}{3}}-1)}^2+{(1.7224)}^2}=2.07$$$$IGH=180-({tan}^{-1}\left(\frac{l}{2}\right)+{tan}^{-1}\left(\frac{l-1}{\sqrt{3}l-2}\right))=99.23$$$$\left[IGH\right]=\frac{1}{2}\times sin(99.23)\times 2.07\times 2.936=3$$

Commented by Subhi last updated on 22/Jun/23

Commented by Mingma last updated on 22/Jun/23

Perfect ��

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