Q. 225.0( 1 Vote )

Using integration, find the area of the region bounded by the triangle whose vertices are
(i) ( – 1, 2), (1, 5) and (3, 4)

(ii) ( – 2, 1), (0, 4) and (2, 3)  [CBSE 2017]

Answer :

Equation of side AB,


Or


Or 3x + 3 = 2y – 4


Or 2y – 3x = 7


...(i)


Similarly, the equation of side BC,



Or


Or – x + 1 = 2y – 10


Or 2y = 11 – x


(ii)


And equation of side AC,



Or


Or


Or x + 1 = 2y – 4


...(iii)


These are shown in the graph below: -



Area of required region


= Area of EABFE + Area of BFGCB – Area of AEGCA









= 4 sq. units


The area of the region bounded by the triangle is 4 sq. units.

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