Question

In a llgm ABCD , AC and BD intersects at O. If ar(∆AOB)=14.5 cm2,

then ar(llgm ABCD)=_______cm2.​

Answer 1

Answer:

In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB --- ( Alternate angle)

∴ ∠ACB = 32

∘

∠AOB + ∠BOC = 180

∘

--- (straight angle)

⇒70

∘

+ ∠BOC = 180

∘

∴ ∠BOC = 110

∘

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180

∘

⇒∠OBC + 110

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+ 32

∘

= 180

∘

⇒ ∠OBC = 38

∘

∴ ∠DBC = 38

∘