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Question

In figure, DE||BC,DE=3cm,BC=9cmandar(ΔADE)=30cm2.Findarofquad.BCED.
1054880_021f10b855a941f68fac98403772cde1.png

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Solution

Since DEBC,D=B and E=C and
A remains the same.

So by AAA Criteria, we get

ABCADE

Since DEBC=13

ADAB=AEAC=13

So, AB=3AD and AC=3AE

Now area of triangle ABC=12(AB)(AC)=12(3AD)(3AE)=9×12(AB)(AC)

Area of ABC=12(AD)(AE))=9(30)=270 cm2

Now, area of BCDE= Area of ABC Area of ADE=27030=240 cm2

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