The vertex A of `triangle ABC` is joined to a point D on BC. IF E is the midpoint of AD then `ar(triangleBEC)` = ?

Options

A. `(1)/(2)ar(triangleABC)`
B. `(1)/(3)ar(triangleABC)`
C. `(1)/(4)ar(triangleABC)`
D. `(1)/(6)ar(triangleABC)`

Answer

A

Explanation

Median BE in `triangleACD` divides it into two `triangle` of equal area.
`therefore ar(triangleCED)=(1)/(2)ar(triangleACD)`.
`thereforear(triangleBED)+ar(triangleCED)=(1)/(2){ar(triangleABD)+ar(triangleACD)}=(1)/(2)ar(triangleABC)`
`rArr ar(triangleBEC)=(1)/(2)ar(triangleABC)`.