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.
