In `triangleABC`, it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then, `ar(triangleBOE)` = ?

Options

A. `(1)/(3)ar(triangleABC)`
B. `(1)/(4)ar(triangleABC)`
C. `(1)/(6)ar(triangleABC)`
D. `(1)/(8)ar(triangleABC)`

Answer

D

Explanation

Median AD divides `triangleABC` into two `triangle` of equal area.
`therefore ar(triangleABD)=(1)/(2)ar(triangleABC)`.
Median AE divides `triangleABD` into two `triangle` of equal area.
`therefore ar(triangleABE)=(1)/(2)ar(triangleABD)=(1)/(4)ar(triangleABC)`.
Median OB divides `triangleABE` into two `triangle` of equal area.
`therefore ar(triangleBOE)=(1)/(2)ar(triangleABE)=(1)/(8)ar(triangleABC)`.