A glass panel for a roof lies in a plane that meets the three coordinate axes at the points A, B…

Step 1. The intercepts. $\dfrac{a}{3} = 1$, $\dfrac{b}{3} = 2$ and $\dfrac{c}{3} = 3$. So $a = 3$, $b = 6$ and $c = 9$. The $z$-intercept is $9$ metres.

Step 2. The plane. $\dfrac{x}{3} + \dfrac{y}{6} + \dfrac{z}{9} = 1$. Multiply by $18$: $6x + 3y + 2z = 18$. So $k = 18$.

Step 3. The distance. $\dfrac{18}{\sqrt{36 + 9 + 4}} = \dfrac{18}{7} \approx 2.571$ metres.

Step 4. The area. $\overrightarrow{AB} = (-3, 6, 0)$ and $\overrightarrow{AC} = (-3, 0, 9)$. Their cross product is $(54, 27, 18)$ with length $\sqrt{2916 + 729 + 324} = \sqrt{3969} = 63$. The area is $\dfrac{63}{2} = 31.5$ square metres.