BdMO National Primary 2015#6

[samiul_samin]

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

[samiul_samin]

Hint

Screenshot_2019-02-22-22-03-48-1-1.png

All of the equilateral triangles have same area.
Find symmetry.

Answer

$\fbox {96}$

Solution

After a bit drawing we can see that
$[AFJE]=[BKLGNM]+[CMNHPO]+[DOPIRQ]+[BMC]+[COD]+[DEQ]+[RJI]+[IPH]+[HNG]+[IFG]+[KAB]\Rightarrow [AFJE]=4[BKLGMN]=4×24=96$