Problem: Given parallelogram ABCD with E the midpoint of diagonal BD. Point E is connected to a point F in DA so that DF=31DA. What is the ratio of the area of triangle DFE to the area of quadrilateral ABEF?
Answer Choices:
A. 1:2
B. 1:3
C. 1:5
D. 1:6
E. 1:7
Solution:
Since DF=31DA, area (△DFE)=31 area (△DEA). Since E is the midpoint of DB, area (△DEA)=21 area (△DBA). Therefore, area (△DFE)=31⋅21 area (△DBA)∴ area ( quad. ABEF)=65area(△DBA) ∴ area (△DFE): area (quad. ABEF)=1:5.