Question

In the given figure, ABCD is a parallelogram
DE I AB and BF 1 AD. If AB = 12 cm, FL
DE = 6 cm and AD = 9 cm, find BF.​

Answer 1

Answer:

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⇒ In given figure ABCD is a parallelogram.

⇒ AB=DC=6cm and AD=BC=3cm ---(1) [Opposite sides of parallelogram are parallel and equal]

⇒ We can see in figure DE ⊥ AB

⇒ So, area of parallelogram ABCD with height DE and baseAB is,

⇒ Area of parallelogram ABCD =

2

1

×AB×DE

⇒

2

1

×6×4 [From ( 1 )]

∴ Area of parallelogram ABCD=12cm

2

----- ( 2 )

⇒ In figure BF⊥AD

⇒ So now we can take BF as a height and AD as a base.

⇒ Area of parallelogram ABCD=

2

1

×AD×BF

⇒ 12=

2

1

×3×BF [From ( 1 ) and ( 2 )]

⇒ BF=

3

24

∴ BF=8cm

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