Question

medians of triangle PQR intersect at O. show that ar(POQ)=1/3 ar(PQR)

Answer 1

HEY MATE!!!

GIVEN:- IN TRIANGLE PQR and O is the point of intersection of median

To proof ar(POQ) = 1/3 ar( PQR)

solution :- In triangle PQR

PD is the median

ar ( PDQ ) = ar ( PDR) median divides the triangle into two triangle with equal areas

arc ( PDQ ) - ar ( QOR) = ar ( PDR) - ar( QOR) subtracting area of QOR from LHS and RHS

ar ( POQ ) = ar ( POR) ---- 1

RF is the median

ar( PRQ) = ar ( FRQ ) median divides the triangle into two triangle with equal areas

ar( PRQ ) - ar ( POF ) = ar ( FRQ ) - ar ( FOQ)

ar ( POQ ) = ar ( QOR)-----2

From 1 and 2 we get,

ar ( POQ) = ar ( QOR) = ar ( POR) = ar ( PQR)

ar ( POQ) = 1/3 ar (PQR)

diagram is attach

HOPE IT HELPS YOU!!!