In the given figure ABCD, DCEF and ABFE are parallelograms. Show that ar(∆ADE) = ar(∆BCF).

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Solution

In ∆ADE and ∆BCF, we have:
AD = BC (Opposite sides of parallelogram ABCD)
AE = BF (Opposite sides of parallelogram ABFE)
DE = CF (Opposite sides of parallelogram DCEF)
i.e., ∆ADE ≅ ∆BCF
∴ ar(∆ADE) = ar(∆BCF)

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