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)

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.