In a parallelogram PQRS, L and M are the mid-points of QR and RS respectively. Prove that :
ar( ΔPLM) = 3/8 ar( IIgm PQRS).
Please help. :)
PQRS is a parallelogram. L and M are the mid point of sides QR and RS respectively.
Join SQ and draw LN || PQ.
In ΔSRQ,
L and M are the mid point of sides QR and RS respectively.
It can be proved that,
We know that, a diagonal of a parallelogram divides it into two triangle of equal area.
area (|| gm PQLN) = area (|| gm SRLN) [Parallelograms on equal base (LQ = LR) and between the same parallels are equal in area]
Similarly,
area (ΔPLM)
= area (|| gm PQRS) – [ area (ΔLMR) + area (ΔPQL) + area (ΔPMS)]