Calculate the area bounded by the lines: x + 2y = 2, y – x = 1 and 2x + y = 7.

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 .

Given;

The lines x + 2y = 2, y – x = 1 and 2x + y = 7.

By solving these equations, we get the points of intersection as (0,1), (2,3) and (4,-1).

Required area

=3 + (24 − 12) − (12 − 3) = 6 sq.units