In , and are the midpoints of and . Lines through and drawn parallel to and…

MATHEMATICS · Single correct · CBSE · Mathematics · Quadrilaterals · Quadrilaterals

Problem

\triangle ABC

D

and

E

are the midpoints of

AB

and

AC

. Lines through

D

and

E

drawn parallel to

AC

and

AB

respectively intersect at

F

, forming quadrilateral

ADEF

. If the area of

\triangle ABC

100\,\text{cm}^2

, the area of quadrilateral

ADEF

is (a)

25\,\text{cm}^2

(b)

75\,\text{cm}^2

(c)

50\,\text{cm}^2

(d)

33\dfrac{1}{3}\,\text{cm}^2