Question

The midpoints of the sides of a triangle along with any of the vertices as the fourth point makes a parallelogram of area equal to

(a) $\frac{1}{2}\left(ar△ABC\right)$

(b) $\frac{1}{3}\left(ar△ABC\right)$

(c) $\frac{1}{4}\left(ar△ABC\right)$

(d) $\left(ar△ABC\right)$

Answer 1

D, E and F are the midpoints of sides BC, AC and AB respectively.
On joining FE, we divide △ABC into 4 triangles of equal area.
Also, median of a triangle divides it into two triangles with equal area
ar(AFDE)=ar(△AFE)+ar(△FED)
=2ar(△AFE)=
=2×ar(△ABC)=ar(△ABC)
Hence, the correct answer is option (a).