BdMO National Primary 2015#6

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Primary 2015#6

Unread post by samiul_samin » Tue Feb 19, 2019 10:33 am

In the following figure $BKLGNM$, $CMNHPO$ and $DOPIRQ$ are regular hexagons (all six sides of each hexagon are equal and so are the angles). $ BKLGNM$ has an area of $24$ square units. What is the area of the rectangle $AFJE$?
Screenshot_2019-02-19-10-22-39-1.png
Screenshot_2019-02-19-10-22-39-1.png (13.09 KiB) Viewed 967 times

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samiul_samin
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Joined: Sat Dec 09, 2017 1:32 pm

Re: BdMO National Primary 2015#6

Unread post by samiul_samin » Sat Feb 23, 2019 11:54 am

Hint
Screenshot_2019-02-22-22-03-48-1-1.png
Screenshot_2019-02-22-22-03-48-1-1.png (8.62 KiB) Viewed 954 times
All of the equilateral triangles have same area.
Find symmetry.
Answer
$\fbox {96}$
Solution
After a bit drawing we can see that
$[AFJE]=[BKLGNM]+[CMNHPO]+[DOPIRQ]+[BMC]+[COD]+[DEQ]+[RJI]+[IPH]+[HNG]+[IFG]+[KAB]\Rightarrow [AFJE]=4[BKLGMN]=4×24=96$


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