The mid points of the sides of a triangle `A B C` along with any of the vertices as the fourth point make a parallelogram of area equal to:
(a)`a r\ ( A B C)` (b) `1/2a r\ ( A B C)` `1/3a r\ ( A B C)` (d) `1/4\ a r\ ( A B C)`

Explanation

D, E and F are the midpoints of sides BC, AC and AB respectively.

On joining FE, we divide `triangleABC` into 4 triangles of equal area.

Also, median of a triangle divides it into two triangles with equal area.

ar(`AFDE`)=ar(`triangleAFE`)+ar(`triangleFED`)

2ar(`triangleAFE`)=`2xx1/4`ar(`triangleABC`)

`1/2`ar(`triangleABC`)

Hence, option(b) is correct.