Question

In the given figure, ABCD is a parallelogram. If E AND F are midpoints of BC and AD respectively, then which of the following statements is correct?

Answer 1

ABCD is a parallelogram ....(given)
E is the midpoint of BC and F is the midpoint of AD ..... (given)
Therefore, BE = EC = AF = FD

BEFA and ECDA are parallelograms ....
Therefore, area of //gm ACEF = area of //gm ECDF ..... (i) (parallelograms having equal bases and between the same parallels are equal in area)

Area $\Delta DEF=\frac{1}{2}$ area //gm ECDF ..... (area of triangle is half the area of parallelogram if they have the same base and between the same parallels)

Area $\Delta DEF=\frac{1}{2}$ area //gm AFEB ..... (from(i)).... (ii)

Area $\Delta ABE=\frac{1}{2}$ area //gm AFEB ..... (area of triangle is half the area of parallelogram if they have the same base and between the same parallels)

Therefore Area $\Delta ABE$ = Area $\Delta DEF$ ..... (from(ii))

Area $\Delta AED\frac{1}{2}$ area //gm ABCD ….(area of triangle is half the area of parallelogram if they have the same base and between the same parallels)