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In the adjoing figure, two parallelogram...

In the adjoing figure, two parallelograms ABCD and AEFB are drawn on opposite sides of AB. Prove that
`ar("||gm ABCD") +ar("||gm AEFB")`
`=ar("||gm EFCD")`.

Text Solution

Verified by Experts

In `triangle`AED and `triangleBFC`, we have
AD = BC, AE = BF and DE = CF (opp. Sides of a ||gm).
`therefore triangle AED cong triangleBFC.`

So, `ar(triangleAED)=ar(triangleBFC)." "...(i)`
`ar("||gm ABCD")+ar("||gm AEFB")`
`=ar("||gm DEFC")+ar(triangleAED)-ar(triangleBFC)`
`=ar("||gm EFCD")` [ using (i)].
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