Proof for area of an obtused angled triangle

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Let us consider an obtuse angled triangle ABC as shown below.

Now draw a perpendicular line segment AD and extend line segment BC as shown below.
From the above figure,Area of triangle ABC = Area of triangle ADC - Area of triangle ADB

From the fact that, 

Area of a right angled triangle = (1/2)×Base×Height --------(1)

Area of triangle ADC = (1/2)×DC×AD -------(2)

Area of triangle ADB = (1/2)×DB×AD --------(3)

Therefore,

Area of triangle ABC =  (1/2)×DC×AD - (1/2)×DB×AD [From (1),(2) and (3)]

 Area of triangle ABC = (1/2)×(DC-DB)×AD

 Area of triangle ABC = (1/2)×BC×AD [Since from figure, (DC-DB) = BC]



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