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Question

In parallelogram ABCD, E is mid-point of side AB and CE meets the diagonal BD at point O.
If area of ΔEOB=80cm2. Calculate the area of parallelogram ABCD.

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Solution

From the figure,
EOBCOD
The corresponding sides are proportional.
EBCB=OEOC=12
ar(EOB)ar(COD)=(EOCO)2
ar(COD)=80(4)=240cm2
The area of triangle BOC be y.
The area of two triangle between the two parallel lines are equal. So,
ar(EDC)=ar(BDC)
ar(EOD)+240=240+y
ar(EOD)=y
Similarly, ar(ADE)=ar(BCE)
=80+y
2ar(BCD)=ar(ABCD)
2(240+y)=(240+4)+(80+y)+(80+y)
y=80
ar(ABC)=ar(BCD)
240+80=320cm2
ar(ABCD)=3ar(ABC)=960cm2
Hence, the answer is 960cm2.


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