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.