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

Here we have to find the area of the triangle whose triangle are A(2,1), B(3,4) and C(5,2) as shown below.

The equation of AB,

Y = 3x – 5 ...(i)

The equation of BC,

...(ii)

The equation of AC,

Now the required area (A) =

[(Area between line AB and x - axis) - (Area between line AC and x - axis) from x = 2 to x = 3]

+ [(Area between line BC and x - axis) - (Area between line AC and x - axis) from x = 3 to x = 5]

The area of the region bounded by the triangle whose vertices are (2,1), (3,4) and (5,2) is 4 sq. units