ABCD is a parallelogram Question is (Pink Area)/(All area)=? (Ratio)

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1 Answer
Jun 2, 2018

#E)" " 18#

Explanation:

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Let #|ABC|# denote area of #ABC#,
let #color(red)(|ABCD|=18a), => |ABD|=(18a)/2=9a#,
as #DE:DA=1:3, => |EBD|=1/3*|ABD|=1/3*9a=3a#
#=> color(red)(|EBKD|)=2*|EBD|=2*3a=color(red)(6a)#
Now, draw lines #EM and KQ#, parallel to #AL and FC#, as shown in the figure.
#=> DeltaDEM and DeltaDAN# are similar,
#=> DE:EA=DM:MN=1:2#,
let #DM=w, => MN=2w#,
similarly, #BQ=w, KP=2w#
#DeltaDNL and DeltaDPC# are similar,
#=> DL:LC=DN:NP=3:1#
as #DN=3w, => NP=w#
#=> "shaded area"=1/6*|EBKD|=1/6*6a=a#
Hence, #|"shaded area"|/|ABCD|=a/(18a)=1/18#