**Correct option is (C) \(\frac{ab}{2}\)**

Given line is \(\frac{x}{a} + \frac{y}{b} =1\)

\(\therefore\) x-intercept of line is a & y-intercept of line is b.

Since, both coordinate is perpendicular to each other.

\(\therefore\) Triangle formed by line \(\frac{x}{a} + \frac{y}{b} =1\) & coordinate axes is a right angled triangle.

In right \(\triangle OAB,\)

OA = x-intercept of line = a,

OB = y-intercept of line = b

\(\therefore\) Area of triangle \(\triangle AOB\) \(=\frac12\times OA\times OB\)

\(=\frac12ab\) square units

Hence, area of triangle enclosed by the axes & the line \(\frac{x}{a} + \frac{y}{b} =1\) is \(\frac{ab}{2}\) square units.