Evaluate where, and is a triangular surface with vertices (2,0,0) , (0,2,0) and (0,0,4)

My attempt :

The equation of the triangular plane :

The normal surface vector :

Unit normal surface vector :

Projecting the triangle plane on xy plane,

As the projection is on xy plane, z=0

On integration, S=2

The correct solution however is

Please let me know where my logic is wrong.

Thank you.