The easiest way is using the Stokes theorem if you know that.
let , then
Let S be the surface area enclosed by L, then
Let p be the projection to the xy plain then p is a diffeomorphism on S and let q be its inverse, and Let A=p(S), Note that p(x,y,z)=(x,y), so the pullback q*(dx)=dx, q*(dy)=dy
= = area of A = (area of S) *
Where is the angle of the two planes with normal vectors v=(1,1,1) and w=(0,0,1), so
So the anwser is