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Find the area of parallelogram ABCD if $A E : E B = 1 : 2 .$

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$25 s q m$

$36 s q m$

$45 s q m$

$22.5 s q m$

answer is C.

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Detailed Solution

Concept: In parallelogram

ABCD, AB=CD=9cm (Opposite sides of a parallelogram are equal)

Now, AE:EB=1:2 and AE+EB=AB

⇒K+2K=9 ⇒K=3 ⇒AE=3 cm

In ΔAED,AD2=AE2+ED2(By Pythagoras theorem)

⇒52=32+ED2 ⇒ED2 = 25-9 ⇒ED=4 cm

Now, Area of parallelogram ABCD=Base× corresponding altitude =AB×DE =9×4 =36Sqm.

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