Given:

x + y − 6 = 0 … (1)

x − 3y − 2 = 0 … (2)

5x − 3y + 2 = 0 … (3)

Assuming:

In triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively.

Concept Used:

Point of intersection of two lines.

Explanation:

Solving (1) and (2):

x = 5, y = 1

Thus, AB and BC intersect at B (5, 1).

Solving (1) and (3):

x = 2, y = 4

Thus, AB and CA intersect at A (2, 4).

Similarly, solving (2) and (3):

x = −1, y = −1

Thus, BC and CA intersect at C (−1, −1).

∴ Area of triangle ABC =

Hence, area of triangle ABC is .