(b) $\dfrac{1}{2}ab$
The line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ meets the x-axis at $(a, 0)$ and y-axis at $(0, b)$, forming a right triangle with base $a$ and height $b$. Area $= \dfrac{1}{2} \times a \times b = \dfrac{1}{2}ab$.
The intercept form of a line directly gives the x-intercept as $a$ and y-intercept as $b$. The triangle formed with the coordinate axes is right-angled at the origin, so the standard formula Area $= \frac{1}{2} \times \text{base} \times \text{height}$ applies directly. Note: $a$ and $b$ must be positive for the area to be positive; the formula gives $\frac{1}{2}|ab|$ in general.