In 
, P divides the side AB such that AP : PB = 1 : 2. Q is a point in AC such that 
. Find the ratio of the areas of 
and trapezium BPQC.
We know
PQ∥BC
1= AP
2 PB
In 
∠A=∠A [Common]
∠APQ=∠B [Corresponding angle]
ABC
APQ
Area(
) =AP2
Area (
) AB2
ar (
)___________ = 12/32
ar(
)+ar(
)
9ar(
)= ar(
)+ar(
)
9ar(
)- ar(
)=ar(
)
8ar(
)=ar(
)
ar(
) = 
ar(
)
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