In A ` A B C ,\ P\ a n d\ Q` are respectively the mid-points of `A B\ a n d\ B C` and R is the mid-point of `A Pdot` Prove that: `a r\ ( R Q C)=3/8\ a r\ (\ A B C)`

Explanation

Solution: As we know that `angleR` is a median of `triangleCAP`

`therefore` ar(`triangleARC`)=`/2`ar(`triangleCAP`)

`1/2xx1/2`ar(`triangleABC`)

=`1/4`ar(`triangleABC`)

Since RQ is a median of `triangleRBC`

`therefore` ar(`triangleRQC`)=`1/2`ar(`trianglerBC`)

`1/2`ar(`triangleABC-triangleARC`)

`1/2`ar(`triangleABC-1/4triangleABC`)

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