Question

In the given figure, ABCD is a parallelogram. E and F are midpoints of BC and AD respectively. The ratio of area $\Delta AFE$ : area of parallelogram ABCD is

• A. 8 : 1
• B. 4 : 1
• C. 1 : 4
• D. 1 : 8

Answer 1

The correct option is C

1 : 4

(i) ABCD is a parallelogram ..... (given)

(ii) E is mid point of BC and F is midpoint of AD ..... (given)

(iii) Therefore, BE = EC = AF = FD

(iv) BEFA and ECDA are parallelograms ..... (one pair of opposite sides are equal and parallel)

(v) Therefore, area of parallelogram ACEF = area of of parallelogram ECDF = $\frac{1}{2}$ Parallelogram ABCD.... (parallelograms having equal bases and between the same parallels are equal in area)

(vi) Area AFE= $\frac{1}{2}$ area of parallelogram ABEF……. (area of triangle is half the area of parallelogram if they have the same base and between the same parallels)
$=\frac{1}{2}\times \left[\frac{1}{2}\text{area of parallelogram ABCD}\right]$
$=\frac{1}{4}$ area of parallelogram ABCD