Using integration

Given;

The triangle whose vertices are (2, 5), (4, 7) and (6, 2).

Let A(2,5), B(4,7) and C(6,2)

⇒ The equation of AB is

⇒ The equation of BC is

⇒ The equation of CA is

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Required area

= 7 sq.units