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Question

E is the midpoint of diagonal BD of a parallelogram ABCD. If the point E is joined to a point F on DA such that DF=13DA, if the ratio of the area of ΔDEF to the area of quadrilateral ABEF is 1:K then find K ?

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Solution

ABCD is a parallelogram.E is the midpoint of BD.E is joined to F,where FD=13DA

Draw BPAD and EQAD

BPEQ

In BPD,

E is the midpoint of BPandEQBP

Q is the midpoint of BD

EQ=12BP

AreaofABD=12ADBP

AreaofEFD=12DFEQ

AreaofEFDAreaofABD=12DFEQ12ADBP=1213AD12BP12ADBP=16

AreaofEFD=16AreaofABD

AreaofquadrilateralABEF=AreaofABDAreaofEFD=AreaofABD16AreaofABD=56AreaofABD

AreaofEFDAreaofquadrilateralABEF=16AreaofABD56AreaofABD=15

The ratio is 1:5

1182639_1101396_ans_8d484caaa6e34ccfaf11ac2231a19300.png

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