Question

MNOP is a parallelogram . Q and R are point on sides MN and ON respectively . if ar(PRM) =12 cmsquare , find ar(POQ)

Answer 1

we have given that MNOP is a parallelogram.

since parallelogram MNO and triangle PRM are on the same base PM and between same parallels PM and ON

∴ ar (ΔPRM) =1/2 ar(║MNOP) ......(1)

similarly ║MNOP and triangle PQO are on the same base PO and between same parallels  PO and MN

∴ ar (ΔPQO ) = 1/2ar(║MNOP)........(2)

from equation 1st and 2nd 

ar (ΔPQO) =ar(Δ PRM)
ar(ΔPQO)  = 12 cm²                  (∵ ar(ΔPRM) = 12 cm ²)

Answer 2

Ar ΔPRM = 1/2 ar of ║gram MNOP .(∵triangle and parallelograms with the same base and between same parallels have half the area of the parallelogram) ∴ar llgram MNOP = 2 x ar ΔPRM = 2 x 12sq cm = 24sq cm ar ΔPOQ = 1/2 ar llgram MNOP( ∵ΔPOQ and llgram MNOP lie on the same base and between same parallels.) Ar ΔPOQ = 1/2 x 24 = 12 sq cm.