# If E,F,G AND H ARE RESPECTIVELY THE MID POINT OF THE SIDES OF A PARALELLOGRAM ABCD SHOW THAT ar(EFGH) = HALF OF ar(ABCD)

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by vasuChauhan

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by vasuChauhan

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⇒ Draw a line HF which should be parallel to CD and AB.

⇒ Ar. ( EFGH ) = Half of . Ar ( ABCD )

⇒ We know that

⇒

⇒ Now in ,

Hence ,

⇒

⇒ ( Equation - 1 )

⇒ Also,

So

⇒

⇒Also ,we know that

Hence,

⇒Ar .( EFH ) + Ar. ( GFH ) = 1 / 2 Ar. ( ABFH ) + 1 / 2 Ar .( DCFH )

⇒Ar. ( EFGH ) = 1 / 2 ( Ar. ( ABFH ) + Ar. ( DCFH )

⇒Ar . ( EFGH ) = 1 / 2 ( Ar.( ABCD )

⇒Ar. ( EFGH ) = 1 / 2 Ar (ABCD)

⇒

⇒