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In regular octagon ABCDEFGH,  M and  N are midpoints of  line BC and  line FG respectively. Compute [ABMO]/[ABCDEFGH]. ([ABCD] denotes the area of polygon ABCD.)

 

 Aug 3, 2022
 #1
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Draw BO  and CO

 

[ABO ]  = (1/8)  of the octagon's area

 

[BCO ] =  (1/8) of the octagon's area

 

And 

 

[BMO ]  = (1/2) [ BCO ] =   1/16  of the octagon's area

 

And  [ ABO ] + [ BMO ]  =   [ ABMO ]  =   (1/8) + (1/16) =  (3/16) of the octagon's area

 

So

 

[ABMO ] / [ ABCDEFGH]  =  3 / 16

 

cool cool cool

 Aug 3, 2022

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