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Question Number 71149 by naka3546 last updated on 12/Oct/19

Commented by MJS last updated on 17/Oct/19

$$\mathrm{if}\mathrm{the}\mathrm{hexagon}\mathrm{is}\mathrm{regular}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{symmetric}$$$$BE\mathrm{is}\mathrm{the}\mathrm{symmetry}\mathrm{axis}$$$$M\in \left(BE\right)$$$$A=C^{\prime }\wedge F=D^{\prime }$$$$\Rightarrow \left(AF\right)={\left(CD\right)}^{\prime }\mathrm{and}\mathrm{similar}\mathrm{for}\mathrm{all}\mathrm{pairs}\mathrm{of}\mathrm{lines}$$

Commented by naka3546 last updated on 12/Oct/19

$$Shadedareais...$$

Commented by MJS last updated on 13/Oct/19

$$M\in BE\Rightarrow \mathrm{we}\mathrm{get}3\mathrm{pairs}\mathrm{of}\mathrm{symmetric}\mathrm{triangled}$$$$\Rightarrow \mathrm{areas}MAB,MCD,MEF\mathrm{are}\mathrm{the}\mathrm{same}\mathrm{as}$$$$\mathrm{areas}MBC,MAF,MDE$$

Commented by naka3546 last updated on 14/Oct/19

$$howtoprovethemaresymmetrictriangled?$$

Answered by MJS last updated on 12/Oct/19

$$\mathrm{shaded}\mathrm{area}\mathrm{is}\mathrm{half}\mathrm{of}\mathrm{the}\mathrm{hexagon}$$

Commented by naka3546 last updated on 13/Oct/19

$$coulditprovedifshadedareaisahalfhexagone?$$

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