E is the midpoint of diagonal BD of Parallelogram ABCD.If the point E is joined to a point F on DA such that DF= 1/3 of DA ,then ratio of th area of triangle DFE to area of quadrilateral ABEF is

a) 1 : 3 b) 1 : 4 c) 1 : 5 d)2 : 5

ABCD is a parallelogram. E is the mid point of BD. E is joined to F, where FD .

Draw BP ⊥ AD and EQ ⊥ AD.

Since BP ⊥ AD and EQ ⊥ AD,

∴ BP || EQ

In ΔBPD,

E is the mid point of BP and EQ || BP.

∴ Q is the mid point of PD. (Converse of mid point theorem)

Area of quadrilateral ABEF = Area of ΔABD – Area of ΔEFD

Thus, the ratio of area of ΔDFE to area of quadrilateral ABEF is 1 : 5.

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