Question

ABCD is a parallelogram, E and F are the midpoints of AB and CD respectively then the ratio of areas of AEFD and EBCF is ______ .

• A. 1:3
• B. 1:1
• C. 1:2
• D. 2:1

Answer 1

The correct option is B 1:1

In parallelogram ABCD
AE || DF, AE = DF
$\because AB=DC\Rightarrow \frac{1}{2}AB=\frac{1}{2}DC\Rightarrow AE=DF$
Therefore, AEFD is a parallelogram.
similarly we can prove that EBFC is a parallelogram.

We know that parallelograms lying on same/equal bases and between same parallels are equal in area.
AE = EB (Since E is the midpoint of AB)
Parallelograms AEFD and EBCF lie on equal bases AE and EB and same parallels AB and DC, therefore area of AEFD and EBCF are equal.
Ratio of areas of AEFD and EBCF is 1:1.