Find a parametrization of the surface: $y + 2z = 2$ inside the cylinder $x^2 + y^2 = 1$.
Then, compute its surface area.
I'm having trouble finding the parametrization of the surface. I don't think it's just $<u, v, 1 - \frac12v>$, but don't know how to relate it to the cylinder.
Write the equation for the plane using cylindrical coordinates: $y+2z=2\implies \rho\sin{\phi}+2z=2$. Solving for $z$ we have,
$$z(\rho,\phi)=\frac{2-\rho\sin{\phi}}{2},~~\text{where}~0\leq\rho\leq1,~0\leq\phi\leq2\pi.$$
Then the surface parametrization is $$\vec{r}(\rho,\phi)=\langle\rho\cos{\phi},\rho\sin{\phi},\frac{2-\rho\sin{\phi}}{2}\rangle.$$