Question

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

Answer 1

`E)" " 18`

Explanation:

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`