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Question Number 74978 by aliesam last updated on 05/Dec/19

Commented by aliesam last updated on 05/Dec/19

$$findtheareaoftheredpart$$

Answered by mind is power last updated on 05/Dec/19

$$\alpha \mathrm{angl}\mathrm{between}\mathrm{blue}\mathrm{and}\mathrm{pink}\mathrm{side}$$$$\mathrm{l}=\mathrm{side}\mathrm{of}\mathrm{hexagon}$$$$\Rightarrow \mathrm{a},\mathrm{b}\mathrm{side}\mathrm{of}\mathrm{retangle}\Rightarrow$$$$\mathrm{a}=\mathrm{lcos}\left(\alpha \right)$$$${\mathrm{h}}^2={2\mathrm{l}}^2-{2\mathrm{l}}^2\cos \left(120\right)={3\mathrm{l}}^2$$$$\Rightarrow \mathrm{h}=\mathrm{l}\sqrt{3}$$$$\frac{\mathrm{l}\sqrt{3}}{\cos \left(\alpha \right)}=\mathrm{b}$$$$\mathrm{s}=\mathrm{ab}=\frac{\mathrm{l}\sqrt{3}}{\cos \left(\alpha \right)}.\mathrm{lcos}\left(\alpha \right)={\mathrm{l}}^2\sqrt{3}$$$$$$

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