Given;

The lines y = 4x + 5, y = 5 – x and 4y = x + 5.

By solving these equations,

y = 4x + 5 …… (1)

y = 5 − x …… (2)

4y = x + 5 …… (3)

From (1) and (2);

4x + 5 = 5 − x

⇒ x = 0; ∴ y = 5 − x = 5

From (2) and (3);

4 (5 − x) = x + 5

⇒ x = 3; ∴ y = 5 − x = 2

From (1) and (3);

4 (4x + 5) = x + 5

⇒ x = −1; ∴ y = 4x + 5 = 1

we get the points of intersection as (0,5), (3,2) and (-1,1).

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